I also find it impossible to believe that Hermione lost to Malfoy, she just beat him fair & square in battle. That certainly sounds like a false memory.

They were pretty evenly matched during the Chapter 78 battle, and Draco was a bit drained from charming all the gloves, so it's by no means impossible that Draco beat Hermoine. I expect if they had 10 duels, each would win at least a few.

But it is true that our only sources regarding the outcome of the duel are Draco and Hermoine's memories along with Quirrell's testimony. If those memories were placed by Hat and Cloak, and if Hat and Cloak is Quirrel, then all of our information about what happened between midnight and 6.33am is based on what Quirrell wants us to know. The only bit that is confirmed by another party is that Draco was indeed at some point unconscious in the trophy room.