You're right to a point, but completely wrong if you are referring to pits and staffies. Quite the opposite, in fact. If you know your dog history well enough, then you know that any fighting dog that had human aggressive tendencies was culled. They had to be handled by humans; their owners, the other dog's owner, the refs, preppers, etc. The dogs also had to be solely focused on the other dog, not the people spectating or working with them.
There is no better breed to compare to a gun than the pits and staffys for this reason.
If that's a staffy it's the shittiest one I've ever seen. What it is, is a fat, aggressive, shitty dog that was unlucky enough to be saddled with some irresponsible owners.
I also noticed the wife/mother ran off. I gave her the benefit of the doubt and assumed possibly she ran off to runoff the dog. Still, I think I would've grabbed my child and insured its safety first.