This is the same Morrison who wrote Batman as being raped by Talia because, as he himself admitted, he forgot how it actually went down in the story he was referencing.
Morrison's shown a great deal of knowledge of Silver and Bronze Age Batman stories, especially the weirder ones, but I haven't noticed many references to more modern material. It might be that they're there and I just don't recognize them, though.
"So now, in every issue of B and R so far, we've seen others refer to Damian as Bruce's true son, inheriting Bruce's traits (even the traits that I don't feel are necessarily handed down in DNA-like 'the desire to do right') and the people telling us these things are the biggest authorities in the Batverse. Alfred--biggest guy possible, really, tells us in issues 1 and 2. Dick--who carefully makes a statement in issue 3 where he refers to Bruce as Damian's father without mentioning his own connection to Bruce. And now in issue 4 we have Gordon--three panels after Damian gets mentioned as a son, Dick gets introduced by Commissioner Jim Gordon, a long-term family friend and the father of the woman Dick dated during his adoption process, as not a son."
I don't see any of those things as downgrading Batman's relationships to the other Robins, to be honest. Dick thought of himself as a ward for his entire childhood, and that's who he was when his relationship with Bruce was cemented and formed. I wouldn't expect him to refer to Bruce as his dad under normal circumstances any more than I would expect him to call him "Dad" instead of "Bruce" when speaking directly to him. That's not to say they don't have a father-son relationship, but so do Alfred and Bruce, and I wouldn't expect Bruce to start calling Alfred "dad" either.
"That said, I like a lot of this book."
Personally, I'm not caring for it. I think I'd like it more if there was more focus on characterization instead of how B & R are such cool and clever crimefighters.