I think it's rather insulting assumption.
Either you haven't spent long enough in the real world, or I've spent too long out there. There are many men who would be flattered by such a comparison. I keep my distance from such people, but they're out there.
Anyways even polite, subtle, well-mannered flirting can quickly turn a night of fun and light gaming uncomfortable when there are multiple people involved. I don't want to end up flirting with the same girl my best friend is flirting with. There's nothing good that can come of that. Someone is going to get their feelings hurt.
As noted by others, this is only true if you're all emotionally immature and passive-aggressive about it. I mean, is this how you behave in other environments? If you both like the same girl, do you make a secret mental competition of it? That doesn't seem very mature to me.
The point is: you could simply choose not to do this. So could your friends. Saying you "couldn't resist" is a cop-out. It's exactly the same as saying "I don't have any control over my behaviour!", and it's on the road towards saying it's the girl's fault that you don't. You do have control. If you don't, then yeah, I don't think you should play with girls. I don't think them being married is going to help, because why would you magically be able to control yourselves there when you couldn't before? The wedding ring isn't a magic item you know. What if she was only in a relationship, not married?
Further, would you really do this session after session? Wouldn't you get over yourselves and remember why you were there? How badly, exactly, are you and your friends feelings going to be hurt when she decides she likes one of you or, more likely from the behaviour described, none of you? I mean again, it seems like you're suggesting immaturity and even maybe a bit of emo-type behaviour should be casually accepted and in no way fought against. I'm not sure that's righteous.