Maxperson
Morkus from Orkus
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."
Those situations are not the same as unconscious. When you are knocked unconscious, you have not had your speed reduced to zero, been knocked prone, or had your ability to move taken away. What that rule is referencing is something like paralysis, where you can't move, but still have your faculties about you to keep in the air if you have a fly spell on. Being knocked unconscious prevents you from being able to think about staying in the air, so you fall.