I think it was implied that the memory wasn't the cause for Harry being able to see Thestrals; Harry seeing Death in the form of a Dementor was. From Chapter 49:

"They are visible only to those who have seen death and comprehended it, a useful defense against most animal predators. Hm. I suppose that the first time you went in front of the Dementor, your worst memory proved to be the night of your encounter with He-Who-Must-Not-Be-Named?"

Harry nodded grimly. It was the right guess, even if for the wrong reasons. Those who have seen Death...