Dude she dated requests her to be his friend on Facebook. She accepts. Am I being paranoid?

I have been dating my girl for over a year. In the first few weeks of meeting her I found out that she went on a date with one of my friends. Because I was just getting to know her and already had a relationship with him I asked him about her. He said that it was just one date and nothing transpired. He actually said she was a good catch and that I should proceed. Cool. He and I are still good friends. The other day he reaches out to her to be his friend on Facebook. She tells me about accepting his friend request after the fact. My first reaction is why is he asking her to be his friend. It's not like we all hang out together. He knows that's my girl and they have nothing in common. I'm old school so I'm thinking there should really be no communication other than pleasantries. Not that I am telling her not to accept his or anyone's request (I'm not a dictator!!), but I would have thought out of respect she should have ran it by me and see if I was OK with it. I really would have been OK with it if she had told me first, but I still would have my suspicions about him. This is a recurring theme with her and guys from her past reaching out and she not shutting them down, in a nice way, because she doesn't see it as a big deal. She is with me and that's all that matters. Thoughts?