This study seems to show that of 134 mammalian bites studied, about 73% were from dog bites both before and after the dangerous dogs act. I don't have full access to the article but the abstract seems to imply that dangerous breed attacks represented a small percentage of the total bite treatments.
I'm not sure it can conclude that the rate of attacks overall stayed the same when dangerous breed ownership rates as a whole reduced. The conclusion seems to be that "dog bites are still a similar percentage of mammalian bites" without regard to the overall rate of dog ownership and the impact of the law on dangerous dog ownership rates specifically (but perhaps it is inside the study?)
One would expect that this sort of statistic would be easy to find if it were true, given the advocacy of bully-breed groups.