This is not accurate. The rules note two situations when the flyer does not fall: when it can hover and when it is held aloft by magic.
"If a flying creature is knocked prone, has its speed reduced to 0, or is otherwise deprived of the ability to move, the creature falls, unless it has the ability to hover or it is being held aloft by magic, such as by the fly spell."
Based on this, it would indeed be difficult to say that RAW is anything other than that the unconscious flyer stays aloft. However, this sort of thing contributes to the dwindling of my respect for 5e's creators. This is the operative part of the description of
Fly.
The target gains a flying speed of 60 feet for the duration.
That is quite a nice, clean description. It
could make adjudication easy, since it implies that the flyer can simply be treated like any other flying creature. But noooo. We are now informed that
Fly 'holds the creature aloft'. What? The spell description says no such thing. The problem I have with this is not the particular specific case covered by the flying rules. Rather the problem is that this now introduces doubt as to extent to which we can treat a
Flying creature in the same way as a flying creature. They have, in effect, invented a new concept -
Flying creature - where none was needed, but failed to give a full explicit accounting of it.
Am I being hypercritical? Maybe. I certainly have been sensitized recently by observing some of the shenanigans (that people assert are) enabled by the XGtE content, and anticipating, based on past performance, that tweeting at Crawford about them will produce a completely random assortment of (no response), (no that doesn't work), and (sure that works). (By 'random' here I mean not discernibly based on any underlying principles or reasoning.)
I used to think that @
CapnZapp was being perhaps a bit whiny. I am coming more to the view, though, that WoTC really does owe us a more carefully considered rule set.