I live in a (very) rural area of Georgia. Several years ago, my wife and I found a flea-infested, month-old pup at our back door. After taking care of the fleas, we decided to keep the pup, not knowing what breed she was. Good feed and a little TLC worked wonders. When the dog approached sexual maturity, we took her to the vet for spaying. The vet told us she looked like "pure" pit bull. And a healthy, well-muscled specimen she was.
Nicer dog you couldn't ask for. Independent, yes. She was not underfoot or "in the way". Very protective of family members, indifferent toward others. Only dog I've ever seen who would smile with her mouth, while waggling her whole body. But then, she would only smile at my wife, never at me or at others.
Your dog reminds me of my neighbor's dog. Only he's a bull terrier mix. I was worried about him being around my children until I realized he was even scared of our little cat. I feel bad for him. He's so skittish and acts like he's always in trouble. When he is in trouble, his owners might give him a tap on his rear, but not hard.