I also believe the memories are coming from the tardis. But the thing to is the tardis is sentient. It thinks for it's self and is connected to the doctor. When he went into the shop, he got cut off from the Tardis. He had trouble recognizing the god. Each time the door opened he would have a moment of recognition as if he was recieving a . My theory is the tardis is giving the doctor back the memories as he needs them to keep from overloading him.

My personal theory is she is similar to the toy maker and the Maestro. Part of the pantheon. Not necessarily a malevolent entity, but someone who makes sure events happen. The theory of her matching up the doctor with companions makes alot of sense, but not in the aspect of of the companions. More as part of who the Doctor is. Each companion, for good or bad, has helped shape the doctor. Taught him lessons. Helped push the Doctor into what he has needed to do and become. A guardian or watcher helping to mold the Doctor towards his own destiny. We have seen times we're he almost gave up, yet due to his interactions with his companions, he found the strength or purpose to carry on and break past his own limits.