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.

Draco is the better duelist at this point. Draco tired himself out by casting all those tough spells someone his age should not even be able to do, let alone do many times in a row. This was pointed out by Quirrel and Madame Bones, which makes it unlikely that it was just Draco rationalizing it.

Hermione is more magically powerful and also more clever, but when it comes to dueling, Draco still probably has the edge.

Maybe Malfoy's first self-defensive instinct was right? Maybe he really had worn himself down by casting all those spells on all those gloves, and that's the only reason he lost. Certainly he thought it was plausible enough that he could beat her that it was worth having a duel as a test.