My first impression was that the OP was over-reacting.
I certainly don't think that that phrase needs to mean anything sinister, especially from family/friends of family.
Of course, only the OP has the full background.
After I read the updates... the 54 year old cousin does come across as a nasty element. Pedophile? Not a clue. But certainly not a nice guy. Again I don't know the background, but if a cousin of mine confronts me about the way I addressed his daughter, I'd want to make sure that I did not mean anything weird there... and I might think he was over-reacting (as I know I'd never approach a youngster in an inappropriate manner) but I would not dismiss him like that.
So, no, I don't like the cousin, for reasons totally separate from the possible (but largely groundless) suspicion of inappropriatedness.
Now, blocking him from FB etc is all great and fine, but what I'd do is talk to my daughter about it, so that she knows why I'm concerned. Without getting carried away and emotional, and talking about stuff that we do not know... what we do know is the guy is an ass.
Teenagers being teenagers, they want to assert themselves, and that causes often conflicts, arguments etc. Treating them with respect helps. You want your daughter to see you as an ally, not a dictator whose rules she does not understand. You want her to trust you. I think that's the best defense. Then you won't need to worry much about whether he tries to contact her or not, because she'd be paying no attention to him, and would tell you if he annoys her.
I hope I didn't come across too much like preaching. I don't want to tell anyone how to raise their kids! That's just my opinion and how I'd approach this. NOthing more.