The actual reason is much cooler.

We can divide tea names into roughly two major groups: tea-type names (English tea, Spanish té, French thé, Italian tè, Dutch thee, German Tee, Latvian tēja, Hungarian tea, Malaysian teh, Javanese tèh, Tegalu ṭī, Sinhala tē, Yoruba tii) and cha- and chai-type names (Turkish çay, Kurdish çay, Greek tsái, Croatian čaj, Portuguese chá, Romanian ceai, Russian chay, Thai chā, Japanese ocha, Korean cha, Hindi chaay, Amharic shayi, Swahili chai, etc.). There are a few other weird things, like the Polish herbata and Burmese lahpet, that don't obviously belong to one or the other (herbata type words are ultimately in the "tea" family but not obviously so) but in many languages the word for tea is from one of those big groups. See this map, where tea-type names are blue and cha and chai-type names are red.

Why? It depends on where people originally got their tea from.

Many people who originally got their tea over land end up with a name ultimately derived from the Mandarin/Northern Chinese chá. You can see this in Persian chay and from there it spread north through Russia into many Eastern European languages (many Slavic languages, Romanian, etc), west through the Middle East (Arabic, Turkish, Kurdish, etc.) and then much of the Muslim World (Swahili, Somali, etc), and southeast into many northern South Asian languages (Urdu, Hindi, Punjabi, etc). This has been reimported into English as "chai", where it means not tea generally but a spiced tea (this is taken from the South Asian term "masala chai") often prepared with heated milk.

Uniquely, Portuguese is not from this overland trade route, but from a southern Chinese shipping route. Portugese chá is related to the Cantonese chàh. The first mention of tea in Europe is apparently a Portuguese book from 1559. Cantonese is the major language of Guangzhou/Canton, and later places like Macau and Hong Kong. Some Asian countries also established sea trade routes with China: Japanese (ocha) and Korean (cha) seem to have been taken directly from Mandarin. There are other Asian languages that are derived from cha appear not to have gone through the Persian "chay" (the -y was added as part of Persian grammar), like Tagalog tsaa and maybe the Bengali cha, but I'm not actually sure of the history of any of those usages, and whether they come ultimately from Mandarin or Cantonese or some other Chinese language.

So then where does the tea-family come from? The Dutch, partially, for Europeans at least. And where did the Dutch get their name? Southeast Asia. It's not totally clear whether the Dutch word was taken from the directly from the Amoy/Min word tê (Amoy is a variety of Chinese spoken in the Fujian province, but also among Chinese diaspora in Southeast Asia) or from the Malay word teh which was ultimately borrowed from a Min dialect. Notice that in Malay, Indonesian, Javanese, etc all have teh. Most European terms for tea not derived from the Persian chay come directly or indirectly through this Dutch borrowing in Southeast Asia.

This borrowing went not only in many Western European languages (English, French, German, Spanish, Italian, Norwegian, Finnish, Hungarian, etc) but also in places where tea was introduced by those colonial powers (Yoruba, Zulu, Maori, Navajo, etc). Some Southern South Asian languages, notably those that have no real connection with the Persianate world, have a tea-derived word, for example tē in Sinhala and tēnīr Tamil (nīr is water). I'm not positive that they didn't have separate trade routes directly with Southeast Asia, but I assume tea was popularized in these regions by the British and as such it's a borrowing from English, as British put great effort into building a domestic market for South Asian tea in the 19th and 20th centuries.

Interestingly, English first borrowed the Cantonese-Portuguese term before adopting wholeheartedly the Amoy-Dutch term. Cha was first recorded in English either in the 1590's (Etymonline) or 1616 (OED), apparently derived from the Mandarin rather than the Cantonese, though I'm not convinced of this entirely (the first recording as "chaa" comes from 1598, in a translation of Jan Huygen van Linschoten published as Discours of voyages into ye Easte & West Indies; van Linschoten's life suggests he learned the word from the Portuguese). The word continues to kick around English, but in very minor ways. The spelling/pronounciation/slang term "char" is from in the 20th century, or possibly slightly earlier, clearly under influence from South Asian languages (possibly this was an entirely new borrowing in the British colonial service).

"Tea", though, as a word and luxury import, apparently only arrives in England in the middle of the 17th century. The word is first recorded in 1655. OED has the note:

According to Meyer, Konversations-Lexikon, the first mention of it in Europe is due to the Portuguese in 1559 (under the name cha); chia is mentioned in Maffei's Historia Indica in 1588. Under the name te, thee, it was imported by the Dutch from Bantam (where brought by Chinese merchants from Amoy) c1610–55; first known in Paris 1635, in Russia (by way of Tartary) 1638, in England about 1650.

A few places I've seen, including Etymonline, mention that tea as a product was first introduced in 1644, though without citation. It's interesting to note that one of the reasons there appears to be such diversity in tea-terms is that it arrives in Europe at roughly the same time through two or three different routes (to Russia overland through Muslims lands along the Silk Road and to Portugal and the Netherlands via sea routes around the Cape of Good Hope).

The earliest English citation uses both terms:

1655 tr. A. Semedo Hist. China i. iii. 19 Chá is a leafe of a tree, about the bignesse of Mirtle; [marginal note] its called also Tay.

However, quickly cha/chai/chia loses out. For part of the sixteenth century tee and tay seem to both be in use in England, for instance:

1664 T. Garway (title) An exact description of the growth, quality, and vertues of the leaf tee, alias tay.

The first spelling of "tea" that the OED records is from 1680, though "tee" and "thea" both exist earlier.

Interestingly, the British later developed their own trade routes with China, largely in Cantonese speaking areas of South China, but never replaced the Amoy/Min-Malay-Dutch term of tea with a more Cantonese cha since, at that point, "tea" was already too ingrained.

Several other places saw similar switches, or have the two terms co-exist. The Polish word for tea, herbata, probably derives from the Latin or Dutch "herba" plus the Dutch "thee" or Latinized "thea", firmly putting it in the "tea" camp. However, the word for tea-kettle in Polish is czajnik, a borrowing from Russian with "chay" clearly in there. In Morrocco, where tea culture is uniquely based on mixing green tea (usually gunpowder tea) with fresh mint leaves, the normal chay derived Arabic coexists with a later borrowing of a tea derived word. People apparently all types of tea can be aš-šāy, but the more common way to refer to the local green-mint tea is it-tay, just as in English "chai" now represents a distinctly prepared subset of all "tea". The current Greek word is tsái but apparently there is a somewhat archaic and formal alternative in téïon. The normal Finnish word is tee, from Swedish, but in Eastern Finland near the Russian border some people apparently colloquial use terms like tsai derived from the Russian chay. For more charts and tables of the different borrowings (with some dubious and contradictory information in the text), see the Wikipedia page for etymology of tea (the above Finnish and Greek examples I only know from Wikipedia, so take them with a grain of salt).

It's a shame that your tour guide gave you a bullshit story when the real story is more interesting. You can see a map of the European etymologies here that really sums it all up. Tea went overland to Eastern Europe (probably from a northern Chinese language like Mandarin, not a southern one like Cantonese as this map says, then via Persian to both Russian and the Ottoman cultural spheres) and by sea to Western Europe (with the Amoy-Dutch or Amoy-Malay-Dutch thee clearly having more success than the Cantonese chá of Portugal). More globally, take a look again at that map from the first paragraph: blue dots are languages with tea-words from the branching Amoy->Malay->Dutch stream; red dots are languages with cha- or chai-words from either the branching chai Mandarin->Persian stream or from another cha-using Chinese language like Cantonese. The etymologies of the words for tea is one of my favorite examples of early globalized trade and, when we bring in styles of how tea is consumed, is a fantastic example of localization and adaption of a global commodity.

If I may suggest a larger point: in the field of urban legends (modern folklore), false etymologies mutate and spread like the flu.

Before the 20th century, it was extremely rare to have coinage of a new word in English based on initials or parts of words. In particular, modern words were not coined starting with For Unlawful Carnal Knowledge/Fornication Under Consent of the King, Port Out Starboard Home, To Insure Prompt Service, and such. There are more patterns of false etymologies: for example, medieval English archers did not indicate distain for the French by raising an unlopped middle finger and shouting "Pluck yew!".

In general, I suggest that, as a rule of thumb (by the way, it's a false etymology to say that it was based on the size of a stick with which it was legal to beat someone) ... where was I? Oh, yes. If someone states the origin of a word, I suggest you should reserve judgment. Unless, as with /u/yodatsracist, they have reliable citations. You can at least decrease the initial skepticism if they say it's derived from [culture/language with which the people were actually in contact] [word that sounds quite like the destination language's version and had more or less the same meaning in both languages].