I don't know if I completely buy that. I mean, even under the Brady Bill people could pack heat. In fact that bill's arbitrary limits on clip capacity pushed people to larger caliber guns (why get a 9mm when a 45mm legally carries the same number of bullets?). We can see that gun violence took a drop after the Brady Bill lapsed in 2004:
What I think happened is 9/11, and the huge amount of sympathy for cops that followed 9/11, emboldened police forces and made them feel justified in being separated some from the community they serve. That combined with the Iraq War gave those forces access to military grade weapons, and took away any sort of social responsibility that would keep cops from running to those weapons.
What I think the Brady Bill lapsing did is normalize a more "serious" class of weapon if you will. I mean, if the local Bubba takes what in 1999 was a military only gun to a range every weekend what is so wrong with the police forces having them? Also the lapsing of that bill obvious had a direct effect on violence in Mexico, which hardened a lot of police forces (especially border ones) who didn't want to see that level of societal instability spill over the border.