In Doctor Who, how does River end up in prison?

I'm not convinced she's in prison BECAUSE she "killed a good man."

In Time of the Angels the Bishop says "you're the only one who can manage him - that's why you're here. But it only works as long as he doesn't know what you are."

Also, the Bishop says the Doctor shouldn't trust River because she kills someone - I don't remember for sure, but I'm thinking he only implies she's in prison because she killed someone.

My theory is that the clerics put her in Stormcage so they could use her to manage the doctor whenever they felt the need. Clearly killing him wouldn't prevent his meddling, since he's a time traveler.

I also think she stays in jail because she promised the doctor she would (she says "I have a promise to keep.") - clearly it's not really any kind of problem for her to get out. Maybe the doctor wants her there so he can easily find her.