There is no controversy. There can be absolutely no doubt whatsoever that the Persians sacked and demolished Athens--the reason that this is the only narrative that you heard is because this is the only narrative that exists. The archaeological evidence alone should be enough to prove that. The Archaic city essentially does not survive, and the Acropolis and other Athenian districts are covered in pits which the Athenians essentially were forced to just sweep the rubble into as quickly as they could and build on top of to prevent their city potentially being taken by an enemy while they were rebuilding. That the cleanup of the remains of the Archaic city were hurried is obvious--the Classical wall is made of Archaic sculpture and rubble swept frantically into the shape of a wall, and the Archaic wells of the city are filled with pottery and rubble that was quickly packed into the wells, where they could be at least out of the way. In fact, the quick cleanup of the sack is archaeologically vital, as it preserves an enormous amount of material from the late Archaic city, albeit in fragmentary state and totally removed from their original locations. Equally obvious is how destructive the capture of the city was. We have Archaic sculpture that has been hacked at or defaced deliberately by a hostile hand, the most famous of which are probably the Acropolis Korai, a collection of female statues that were piously given a ritual burial on the Acropolis after the Persian sack. The rubble heaps left over from the sack are quite extensive, and the Persians quite clearly did a thorough job of demolishing the city

Nor is the textual evidence any less uncontroversial. No text attests to Xerxes' sparing of the city, and frankly it's simply impossible given what we know from archaeology and what we know about what happened in the aftermath of the recapture of the city. No Lydian historian talks about the capture (or supposed sparing) of the city. Actually, there is only one Lydian historian, Xanthus, a rough contemporary of Herodotus' who wrote a history of Lydia of which only a handful of fragments survive. There is no reason to believe that Xanthus wrote about the sack of Athens, and even if he did no fragment or summary of it in other authors exists. Unless of course your girlfriend means Herodotus, in which case the proposal becomes even more absurd--Herodotus was from the Carian city of Halicarnassus, even though he was a Greek, not Lydia, and although Plutarch accused him of being too favorable to the barbarians Herodotus quite unambiguously describes the sack of Athens. The only other author that I can think of that she might be referring to is Ctesias, also from Caria and also a Greek. Ctesias, a physician, purported to be writing a correction of Herodotus, on the basis that Herodotus was a liar and that Ctesias was personal physician to Artaxerxes. In fact Ctesias is a totally unreliable source. Though he claimed to have seen what he was describing he in fact makes simple errors all the time, placing cities in the wrong locations or totally omitting events (he appears to have completely omitted the capture of Babylon), and his account seems in many places either to have skipped entire years or to have basically just paraphrased Herodotus. Most notably, however, if your girlfriend is claiming that Ctesias says that Xerxes spared the city she's simply mistaken--a quotation of Ctesias in Photius tells us that Ctesias wrote that Xerxes took the city and set fire to it, except for the small garrison that held the Acropolis, at least until they fled by night, after which it too was burned. Ctesias describes Xerxes plundering the temple of Apollo at Delphi and stuff, so it's not as though Ctesias thinks that this behavior is uncharacteristic of Xerxes. Besides, what on earth would Xerxes have gained from not sacking the city? Near Eastern leaders regularly boasted of firing the cities they captured and slaughtering the inhabitants, and the only inscription of Xerxes has him thump his chest about destroying the sanctuary of the demons (though I believe the consensus is that this doesn't refer to the Greeks and probably refers to an Egyptian or domestic revolt)--the inscription is nearly impossible to gain any historical evidence from, since it's intentionally vague and mystified, but at the very least we can be sure that destroying the city would have been thought of by Xerxes as the expected thing to do.

In other words, there's exactly zero evidence that the Persians did not destroy the city, and there's such an enormous weight of evidence of all kinds that there can be no reasonable controversy over the Persian sack. I've never seen it questioned once, and I cannot see how it could be questioned without fabricating evidence

The account you learned is correct.

First off Themistocles abandoned the city except for a token garrison (much like the strategy used in Plataea against the besieging Spartans to buy more time). Essentially this evacuation involved all the able bodied men being conscripted into the navy, and all the women and children were evacuated. Now when the Persians did get to Athens this small garrison had entrenched themselves in the defensible Acropolis but were eventually defeated. From there Athens was ordered to be torched.

As more evidence of this destruction (to complement the account from Herodotus), it can shown that the original construction of the Parthenon on the Acropolis was utterly destroyed during the Second Persian Invasion and it wasn't till 447 BCE that the Athenians had enough money coming in to actually start the construction again and finish it which gives evidence of at least some damage that would not be consistent with standard protocol for sparing the city. As further evidence, we have accounts from Thucydides of the controversy between Athens and Sparta when Athens started building new walls in 480 BCE after the Persians left due to theirs being destroyed during the Persian occupation (he also mentions in the same section of the extensive destruction of houses in the city saying that those that were not actively used by Persian officers were demolished). And further on that matter, the Athenians were reported to have demolished houses for building materials to aid in speeding up the building of this wall.

Edit: Evidence for the evacuation of the city can be drawn from the fact that the Battle of Salamis occurred after the occupation of Athens by the Persians. As it would be rather absurd to imagine the Persians being so kind as to allow the Athenians to arm themselves, man their boats, and then sail to battle against the Persian navy. So from this we can extrapolate that a large majority of the able-bodied men were removed from the city to man this navy. From there, we can infer that the women and children were evacuated also as it is only on very rare occasions that a leader purposely abandons the entirety of their city's women and children by withdrawing the whole of the defending force. And in further support of this is the fact that having to feed and house this large population practically negates one of the purposes of the leaving behind a small garrison, that is the equally small use of supplies that allow them to maintain a siege for a long period of time without starving. This is more speculative and should be taken with a grain of salt, but even with the Athenian loyalty to their city-state and the love they had for Themistocles their feelings about the duties owed to family members were even stronger and therefore it is hard to imagine the majority of the city agreeing to behave in a way (as in abandoning their family, by not even trying to protect them) that so contradicted their morals. Even more so since it was very likely that by leaving the city they would have believed they were dooming their families to death, as just prior Xerxes had razed the two Greek cities of Thespiae and Plataea meaning that it was very likely Athens would be treated the same way. Honestly, this whole edit is a bit speculative as most of it is extrapolations but it might be convincing if she does not trust Herodotus and Thucydides.