I mean, there's no proving anything about the hospital because even if someone relatively respectable produced a video saying it came from here or there, everyone could say that it could perfectly easily have been digitally manipulated (doubtless there are already such 'proofs' of both circulating social media already).
I'm afraid, much as I'd wish it otherwise for so many reasons, if Israel is going show itself capable of besieging millions of civilians against all international rules of engagement, that makes it look awfully like a regime that would bomb a hospital.