You guys are really overcomplicating it, I think. There's no reason to doubt the facts that we already know.
She is the Doctor's wife and they're married sometime in the future. One of her many (and enduring) quirks is that she likes to tease him, taking advantage of the fact that their relationship -- much like the Time Traveler's Wife -- is not linear. She knows all kinds of things about him that he doesn't know, and she knows that he won't try to get the information out of her in order to avoid mucking everything up. So why wouldn't she have a little fun with that, and why wouldn't he be mock-annoyed by it all? My wife does similar things to me when she knows something I don't, for crying out loud. She also has the strong personality and intelligence that the Doctor would find attractive (not to mention being human; a race he is all but obsessed with to begin with), and all of these encounters with her prior to their first meeting from her perspective is all building up to their relationship. At which point the Doctor will have the upper hand in the teasing. That's probably why she's having so much fun with it now.
As for the mysterious comment about her shady past? Uhm, hello. She's clearly an Indiana Jones type of character. Grave robbing and the like are probably a regular part of her daily life. And hell, when we first see her in this episode she's committing a crime. The question is what she did that the Bishop would know about (and not mind enough to continue working with her), but which the Doctor would show concern over before he's come to know her or the circumstances properly?
I mean, even the Bishop seemed to be familiar enough with the Doctor. Clearly something happened, and it was something that left a bad taste in the Bishop's mouth (hence his "fly away in your little blue box while I deal with the mess you leave behind" comments), but not a bad enough taste as to lose all respect or even consider him a bad person.
What's more, the two times we've met her, she's been involved in things that are of both an archaelogical and save-the-world kind of affairs. Which fits in perfectly with the kind of woman the Doctor would fall for if you ask me.
That said, there's no reason to suspect that River is anything but who she says she is, let alone all these sinister ideas floating around in the thread. I think it would be more prudent to try and figure out the remaining pieces of the puzzle that exists rather than creating a completely different puzzle based on little to no facts whatsoever (ie, the Time Agency, being a con artist, being a Time Lady, etc.).
