I'm a Chinese learner. This is how I understand your difficulty.
我见过他 could mean I met him before (despite of the frequency), it doesn't indicate whether both of you know each other.
I could say 我去伦敦时，那儿见过David Beckham.
While 我认识他 means I recognize him, obviously I know that person. Yet, it isn't necessarily if he knows me.
You can combine both sentences to clarify both meanings.
他见过我，不过他不认识我。He met me, but he didn't recognize me.
We'll see how the Chinese speakers view on it.