Are some people just very naive?

I’m not taking a shot at women here, understand my question at the end of this summary.

This guy and my girlfriend were in the same class in college. Now the course is done and he texts her every day or two. She describes him as a “friendly-to-everyone” type of guy, but she admits he talks too much. From what I’ve seen when I’m around she just gives him the one-word answers (I.E. “ok”, “cool”, “alright”, nothing to provoke conversation) and he’ll never stop replying until she has to ignore them. Also, he just so happens to run into her at malls near her work at the other end of town. At this point I’ve mentioned to her that he’s starting to bother me. She understands my point, but still thinks that this guy is just “overly-friendly.” About 2 days ago this guy asked her to see a movie with him, of course my girlfriend declined. I have absolutely no worry of her cheating on me, we’re both completely faithful in the relationship. She’s from another province and most of her friends are over there so she wants to make new friends here I assume. However she’s overly trusting of some people and that worries me. My question is:
Do some people really think obsessive guys like these are actually just desperately trying to be your friend, or are you all smart enough to realize that when a guy is trying this hard it means he wants you but you’re too nice to tell him off?

For bonus points, does anyone think I’m getting bothered over nothing or would you have done something by this point?

Edit: There. I changed it to “people” just to be politically correct