I do see what you're saying, but in the context of Dick's actual relationship with Bruce I think the narrative is acknowledging the fact that however much they might consider themselves father and son now, it really can't erase the last fifteen odd years of precedent in which that really wasn't the case.
To me at least it has nothing to do with the fact that Dick was adopted, but everything to do with Bruce's relative youth at the time he took Dick in, and Bruce's respect for the fact that Dick already had a father that he still loved and remembered. Bruce made the decision to adopt Dick when he realized how much having a permanently established connection on paper meant to him, not in an attempt to retroactively re-establish all their previous interaction as something it really wasn't. He set out to be a friend and a mentor and to a certain a father figure, but by the time he was really in the right place to begin to function as a parent Dick was long past the age where he needed one.
By no means does that undermine their connection or obvious love for each other, but to me it does put it in a slightly different category than strictly father/son in the traditional sense. Dick's never called him Dad because Bruce had never really been "Dad," so it makes sense to me that it's not a word Dick would use to describe that relationship to anyone else.
Damian, on the other hand, had almost no relationship to Bruce whatsoever when he was alive and has no way to connect with him on any level other than the probable blood connection. It's something that ultimately means very little, but which has some measure of meaning for Damian, which I think is what Dick is encouraging. A connection to Bruce is a connection to him, after all.
Of course, it's entirely possible that I'm wrong about the authorial motivations that factor into the story, and if that's the case I'll happily eat my words in another issue or two. :D