Nice to see a "wild" Robin coming to hand like that!
We have a resident Robin in our garden, a female, I think (I say that because she doesn't sing, whilst all around others are and that she has been tolerant of another robin which occasionally comes into the garden.) We have watched this robin grow up from a speckled juvenile this year.
Earlier in the summer she started to follow my wife around as she gardened. I took some worms and centipedes to her one day as she sat in our holly. At first she didn't come too close, but after a day or so she came right up to me and took an offering. Within a week she was eating regularly out my hand (see photo).
It has got to the stage where she sits on the fence now and "cheeps" for a feed! If she sees us in the kitchen she will fly up to the window and hover for a bit before perching on one of the hanging baskets by the back door. Of course, we have to go out and feed her!
We feed her sunflower hearts and fat from the fat balls, although she is perfectly able to feed herself from the balls and the feeders! (She doesn't know it, but I've watched her from an upstairs window; I think she thought we weren't around!)
Two weks ago, Derwent May in The Times wrote that robins only follow humans because they know that they will dig up food which they can pick up. They also follow other birds which forage on the ground doing exactly the same thing.
I think it goes a bit farther than that. In our garden there are tits, house sparrows, dunnocks, wrens, blackbirds and collared doves, to name a few, and they are all used to the human (and canine!) presence. Most birds stay put when we go outside and we can get quite close to them. In fact, one collared dove will waddle up to within a couple of feet of us.
However, only the robin "demands" food! And only the robin makes her presence known to us deliberately! I think we should give birds a little more credit for having an ability to choose . . .
And, yes, it is a fantastic feeling to have the trust of a wild creature.