Hope this doesn't come off as mean, but if you wouldn't give a person you like/attracted to a second chance because she rejected you then you are a little thin skinned. Most people don't sort out their feeling right away and need more time to process their feeling. People grow and evolve and don't stay the same forever, they are allow to change their mind, it's natural. The problem she describe isn't that big of a deal, so he is a little enthusiastic but that's not her style, fair enough just talk to him about it. When two people get together there is going to be a lot of trial and error, figuring out what works and what doesn't. If you bail the second they do something minor that you don't like, good luck trying to find a partner in life.

If OP want my opinion, yes, I would go out with someone again even if they initially rejected me.