That would depend, it's a chat on a dating site, there's not much to lose by just enjoying the conversation, if they let their skepticism get the best of them, they could miss out on a potentially nice opportunity.
I believe a certain benefit of the doubt should be afforded, if they can't ascertain if somebody is a bad match online[footnote]Sometimes you can, I've encountered people who started talking about marriage and children right away and sending messages every hour, I ran for the hills.[/footnote] and they get to the point where it's time to meet in person, be smart about it, meet in a public place with lots of witnesses. He would have less to worry about as far as creeps go and if he's worried I'm some sort of gold digger, it would become obvious I'm not when I continuously insist on paying my half of the bill.
Having had a previously bad experience with meeting someone from the internet, I was extremely apprehensive when the conversation turned to going offline, but I'm thankful that I did because I wouldn't have met such a wonderful person had I not.