DBP: I don't think dogsbite.org is a good place to get "good data on which breeds are most often involved in fatal attacks." Dogsbite.org will provide, say, the number of reported pit bull attacks in a given year, but its "statistical" information is riddled with both reporting bias and confirmation bias. The people behind dogsbite.org concede that their mission is to inform people about pit bull attacks. They also claim to be dedicated to "putting the safety of humans before dogs," which would be fine except that they also assert that veterinarians, among many others, are unwilling to do the same, which is just preposterous. More pertinent to the issues you raise, however, is that dogsbite.org does not even purport to provide information on the relative risk posed by pit bulls. Without that data, however, there is no basis to assert that pit bulls pose a greater threat than other dog breeds.
I would suggest looking instead at data from the CDC and the American Veterinary Medical Foundation, AVMF. Both of these organizations have done interesting meta-analyses of research and controlled studies. Among a number of interesting findings made by both organizations is that, over long time scales, the proposition that "breed X causes more human fatalities (or injuries or whatever) than any other" is a moving target. In the mid-1970s, breed X was the German Shepherd; in the late 1970s, breed X was the Great Dane; in that late 1990s, Rottweilers and pit bulls emerged as breed X. The CDC has reported that since 1975, over 30 different breeds have been identified as killing people, including Dachshunds, a Yorkie, and a Lab.
Pit bulls are simply the breed-du-jour. The AVMF research demonstrates that social conformance is at least one of the significant reasons that pit bulls are currently seen as uniquely dangerous: people who want big, vicious dogs choose pit bulls precisely because everyone agrees that they are big, vicious, dangerous dogs. But sooner or later, there will be a new breed X and we will all be talking about what must be done to solve the problem of that breed X.
(Also, why do you suggest "breeding controls for pit bull owners"? I could understand maybe wanting to limit the breeding of pit bulls, but what do you accomplish by limiting the breeding that goes on between owners of pit bulls?)