You are correct. They would.
Why Pit Bull Type Dogs Fail as Police Dogs
https://www.freerepublic.com/focus/f-bloggers/3676319/posts
You always hear the argument that "..pitbulls are used in hunting all the time, hence they have good noses.."
They DO NOT have good noses. Pitbulls do work well with other dogs, and they are used for hunting hogs when there are good scent dogs (Walkers, redbones, etc.) running with them. A good pair of hog-hunting pitbulls will run at the back of the pack and follow the "nose" dogs until they see the hog. Then, the nose dogs will back off and let those pits do what they do best. I've seen two pits head-and-heel hogs that weighed in at 400 lbs or better.