These difficulties are easily addressed by genetic testing of dog breeds that’s commonplace today, but that requires forcing genetic testing of dogs that have attacked people, which I don’t believe is law anywhere at the moment.
Purposefully obscuring breed type is scientific malpractice, and often encouraged in forums on pitbull type dogs e.g. r/pitbulls. If you pay attention to this discourse, you will know there’s an intent to obscure these statistics.
CDC stats seem to be only general and one page of this 28 page report issue: https://www.cdc.gov/mmwr/volumes/72/wr/pdfs/mm7236-H.pdf
More recent work generally supports this old data:
https://www.palermolawgroup.com/blog/what-percentage-of-dog-attacks-are-pit-bulls?hs_amp=true
https://www.dogbitelaw.com/vicious-dogs-and-dangerous-dogs/pit-bulls-facts-and-figures/