Could the ending be... (Spoilers)
An elaborate fake created by Elizabeth?
Somewhere in the middle of the game Elizabeth shows/tells that she can create the events within the universes. It's even showcased when the key appears in her hand, and when Booker leads the rebels as well as when the gunsmith and his wife turned up dead. The objective of this fake is so that she can go back and have an ideal father, which in her vision is Booker.
Thoughts?
A drunk man's words are a sober man's thoughts.