Nah, Jason 2.0 is just a case of people forgetting Jason dyed his hair.
And your evidence for this assertion is, considering that DC did point out wherever it was mentioned (Like "Who's Who") that Jason 1.0 was a blond who dyed his hair.
And why are you taking things Jason says so literal?
Because he says them literally perhaps?
He very clearly resents the Batfamily and I'm sure in his current state he would love to remind himself and his new sidekick that he idolized their current enemy once upon a time.