And the original Jason did (eventually) dye his hair. But not because of Bruce.
The original Jason Todd, circus performer--not the second Jason Todd--dyed his hair because when he was originally created, he happened to look different from the original Robin. Which turned out to not be a great move for DC because the licensing rights to Robin were already, and had for a long time, been sold. So all these schoolboxes and give-away items and years of previous and upcoming materials all had a dark-haired Robin on them. Rather than confuse everybody and not sell as many products and anger the retailers, an editorial decision was made to have Jason dye his hair
Dick Grayson growing up was a big deal, and it was the first time that such a huge character had changed so radically--by growing up. So there were some... changes along the way. Like starting with a light-haired (blond) guy and having him dye his hair black.
It was for the public and the franchise. What Morrison's going on about with it, I have no idea.