Yes, they would have to produce a pedigree or convince litigation-fearing city employees that their dog isn’t a pitbull based solely on it’s appearance. Depending on who complains about your dog and what they told city officials, you could be going up against a brick wall.
It’s great if you trust your government to be compassionate and indulgent, but I know better.
I'll take the judgment of an animal control officer over that of a gang banger.