Also, it could be he's trying to reinforce the "don't remember" spell, which will actively cause anyone who is putting the truth together to prefer an option which means he's NOT Spider-Man, so she'd be more liable to believe a half-baked prevarication (since he had not, as far as he was aware at the time, broken the terms of the spell) than the actual truth. If the spell was in effect his excuse might well have worked.