New guy who says he "had relations" with an NPC

Great question, I am not the master DM, but I have dealt with almost the exact same problem. One of my players (a wizard named Will I think) wanted to have fled the country because of a relationship he had with the Queen. This posed huge problems since the King was (supposedly) the NPC who asked the players to rescue his princess. This would have created very awkward and unavoidable bad moment. (Note: the Players screwed so bad with the story that they never met the king and "accidentally" saved the princess).

All I had to do (and note that I am very inexperienced and haven't worked my Adam muscles that often) is walk through exactly what this meant for the player character. It soon became apparent that the Player did not even want his character to be "that sort of person". It was mainly a spur of the moment idea and I didn't even have to say "no you cannot do that"...
Perhaps if you just walk the player through the implications affecting that character (what this makes his character appear as, how this might affect his characters idealology, etc.). He might want to change all on his own.
Please, as well, take this with a grain of salt since I have only dealt with this once and with one particular person...

Pretty much this. Did you go into details about the innkeeper and her husband? Or was it just a quick one-line of "She's married."?  If it's the latter, it's super-easy to retcon that and say that to everyone else they were thought to be married, but only known to the innkeeper and her husband, they'd split a while ago. Maybe just kept up appearances to save face, or whatever reason you want. If they are NPC's of semi-to-really important, then just have the husband die of some cause while the adventurers are out on a quest.

Those are a couple examples of ways to work around it, say "Yes, and..." to the player who's story idea it was, while at the same time avoiding those "relationship" element dangers that you'd rather avoid. Plus you could maybe work in someday, that the PC finds out they have a kid, etc. Lots of story ripe there, without having the "affair story" come into play immediately.

By the way...this right here is D&D in a nutshell.  Ha ha ha!  It will happen, and the sooner you learn to ad-hoc it on the fly, the better. Best laid plans, and all that.

Thanks to all for the discussion / suggestions! Great stuff! I think I'll just summon a red dragon... j.k.

He said that she said that she never had relations, but what he really said to her was that he never had relations with her. Her husband just thought that he said she never said that she loved him, but she is all right with him as long as he doesn't tell her what he was saying. She is probably wrong...

Glad things worked out, and quite well it sounds. I would definitely keep the player invested and working with you so that you can guide them away from anything you are fully comfortable with. The idea of random slaps definitely makes me think of Jack Sparrow and should make for some hilarious role playing.

You could've gave him a random D&D STD... Something like he gets an itchy crotch which happens when he is trying to roll diplomacy or intimidate and he woukd get a -5 to rolls since he is scratching while he is talking.