According to this video, North American English has a developed hard R that is barely seen in any other language. As a native speaker myself, I've never really noticed its irregularity in context with the rest of the world until recently learning Spanish, and just generally paying more attention to language.
First off, is this video accurate? If it is, what influences existed in North America that could have caused British English-speaking colonists to start to develop such an unusual speech characteristic that is almost nonexistent anywhere else?
This is better suited for /r/linguistics than here, since sound change isn't usually related to historical events*, but I'll give it a go.
What you're calling the "hard r" is called a retroflex approximant in linguistics. The "approximant" part just means that the oral cavity is not closed enough to cause turbulence. The "retroflex" part is what's interesting for your purposes; it means that the tongue is positioned with its tip almost vertical or curled back into the mouth, behind the alveolar ridge (see this diagram). It's true that this consonant is somewhat rare, but not as much as you might think from European languages; it's present in some Brazilian Portuguese dialects, in several languages of India, and is very common in Australian Aboriginal languages - not to mention Mandarin Chinese (although that use of retroflection, called "r-colouring", is more like the simultaneous articulation of the consonant and vowel preceding it - American English does this too with words like "bird"). The linguist in the video claims it "barely exists in any other language on Earth", which is misleading for reasonable values of "barely" - from the phrasing I'd expect one or two languages, which is false.
As to why this sound is present in American English, it's hard to say. We know that Old English's <r> was pronounced /ɾ~r/ (a tap and trill, like Spanish pero and perro respectively), in line with other European languages of the time. At some point in history it turned into an approximant, but it's very hard to know when or where since the orthography remained the same - if anyone knows any more please follow me up on this. This approximant could have been either alveolar (the British <r>, which is pronounced with the tongue further forward toward the alveolar ridge), or retroflex. Since the two sounds are practically indistinguishable (and indeed no language distinguishes them), sound change in either direction is fairly simple. In England itself, West Country English has a retroflex <r>, although I don't know enough about the demographics of American colonists to say whether it descends from there.
Overall, it's very difficult to say which form of <r> developed first (it seems more likely that the retroflex was a development from the alveolar), but they both descend from the same Middle English pronunciation identical to the modern Spanish or Italian /r/. And no, the retroflex approximant is, though not common, not an extraordinary rarity either.
* Actually quite an important point to make - sound change is usually only related to history when large numbers of non-native speakers adopt a language with a different phonological inventory. In most other cases, it's essentially unpredictable - so be wary of historicizing "explanations" of sound changes, especially common ones.
Fun fact! (Speech Pathologist here)... there are two completely correct ways to make the American English /r/. There is the retroflex production which has already been mentioned and the bunched/retracted production where the tongue is humped like a mountain back towards the soft palate. It's usually a pretty even split between the two as far as how many people use each /r/. There are also about 32 different variants of /r/ when accounting for the prevocalic /r/, vocalic "er" (air, ear, ire, or, ar, er), consonant blends (gr, tr, rl, str, pr, etc) and the 3 different word positions (initial, medial, final). Because the American English /r/ is so complex, it's one of the most mispronounced sounds and most often triggers a referral for speech therapy. Most students I see for articulation have difficulty with /r/. The /r/ sound is usually established by the time a child turns 7 or 8 but can emerge around 2 or 3.
As an additional question, I've heard that the hard R is more reminiscent of older English and that the British accents which drop the rhotic sound are a newer phenomenon. Is there any truth to this?
