Animals many times are less complicated than people (and usually have more common sense). I moved into a house once where I "inherited" a cat. The cat showed up one day out of the blue and the previous tenant started feeding him and he never left.
When I moved in I was a bit wary of him, as he had a piece bitten out of one ear, had one eye that looked crooked, and was Siamese -- not my favorite.
But, I kept my word and would feed this guy twice a day. After a bit I would put the food bowl just inside the door and leave him be. He would step inside and eat, then leave. After a while I could bring the food bowl inside about 6 feet. I couldn't close the door and take away his "out", else he would freak out.
After a few weeks of this I could close the door, he would come in and walk around (meowing all the time like he was pissed), and even lay down and sleep, on occasion.
A cat that I was not even going to pet let me pick him up.
I don't think he will ever be a "lap cat", as he has too much emotional baggage, but we became a lot closer than I had thought, and I guess I was glad that I was able to make his life a little nicer.