I was joking about this earlier but in all seriousness, I agree with the rest of you all that this story is very, very strange. I mean, all jokes aside, her position/role/title is sobering. You'd have to be a total wacko or have no awareness to bring up topics of a sexual nature communicating with her unless there was something mutual going on.
This is akin to like walking into a big corporate job day 1 and yelling in front of the HR head "Who's the bimbo blonde over there and does she put out?" I don't know a thing about Mel Tucker. Maybe he's Michael Scott or Todd Packer. But he can't be that dumb, can he?