Just thinking about it, I'd look at it this way. I once read in Popbitch, the gossip site, that David Tennant was doing some advert work a few years ago. During lunch, at the canteen, someone approached him and happened to mention that the kids at a special needs care home where he worked were big DW fans. Apparently Tennant spent his lunchtime in character as The Doctor recording greetings and so forth for the fan to record on his smartphone to play to the kids.
He didn't have to do it, he didn't owe it to anyone to do it and, had he not suggested doing it, I wouldn't regard him as selfish. He just decided to do it out of generosity. But, and maybe I'm comparing apples with oranges, when I contrast that approach to Eccleston's, I feel a lot more well-inclined to DT than to his predecessor.