No, for two reasons.
First, my insurance company will not cover me for liability for a pit-bull.
Second, there is something wrong in the head of a tenant who says to himself: I am a tenant. Landlords don't like to rent to dogs. Most landlrods won't rent to large dogs. No landlords will rent to pit-bulls. Hey, I think I'll get myself a great big pit-bull.
I know wonderful responsible owners of American Staffordshire Terriers (the show version of the Pit). Not one of them is a tenant. They are all home owners.
Every tenant I've ever met that owned a Pit-bull is a sleazeball. The dog I might take (the majority of Pits are nice dogs), the owner, never.
Every tenant "seems" nice, "seems" responsible, has a good excuse for everythig when they are applying. I'd take that pit-bull to indicate that guy has issues.
You can't stop him from canceling insurance and his insurance won't stop you from getting sued. It could be a dog scratch or someone fell down because it scared them to see a Pit-bull inside the fence, and all the jury has to hear is "Pit-bull" and you just lost your case and had the judgement tripled.
Just say no.