I don't have a canon answer, but I'm fairly certain it was NOT anything pedestrian like underwareunderwear - otherwise, many other wizards would have magical flying underwareunderwear, the same way they have invisibility cloaks and flying brooms.
The answer most likely lies in the fact that Quidditch Through the AgesQuidditch Through the Ages is an OLD book, so the information in it is out of date.
It is published (in-universe) well before Voldemort is first shown to be able to fly (as confirmation, the last broom it mentions as far as Nimbus models is "Nimbus 1700" - as we all know, Harry's First year model 2000 came out).
Out of universe, it was published (2001) before Harry Potter and the Order of the Phoenix (2003) as well.
Therefore, its (in-universe) authors - as well as JKR out-of-universe - may have been stating 100% correct facts as of that time, after which the brightest magical student that Hogwarts have ever seen (Riddle, that is) surpassed everyone and figured out such a spell.