Probably not, but public opinion is very different from what can be proven in an actual court of law and that's where the real problem is. Legally, they might not be able to prove anything, but the visceral image, fake though it might be, of Spider-Man killing "a fellow hero" in cold blood out of jealousy or envy would stick in the public's imagination for a long while and more than likely taint (some) people's perception of their friendly neighborhood superhero.