Most of River Song's "The Doctor lies" is about it being her own rule #1 for figuring out what's going on when things don't seem to make sense. If things seem incomplete or impossible, consider first if The Doctor lied about something.
River Song: Rule One: The Doctor lies. So do I.
River: Who told you that?
Amy: He did.
River: Rule one: the Doctor lies.
River: He said no one could save him. But he must have known I could.
The Doctor: Rule one: the Doctor lies.
River: Okay. I'm going to tell you what I probably shouldn't. The Doctor's last secret. Don't you want to know what he whispered in my ear?
Amy: He whispered his name.
River: Not his name, no.
Amy: Yeah it was. He said it was.
River: Rule one?
Amy: The Doctor lies.
Gora: You're in violation of rule one. Get over that kicker.
Never take a Favor...you get no money out of it
Everything....and everyone has a price....
This is Rule one