I depends completely on the dog and its past.
Two of our dogs are shelter dogs.
Ethan(whippet mix), is exactly what your mother described... well, not exactly, but similar. He is absolutely terrified about particular things, and will bite. He's been to many many homes, but none worked out because he goes through stages. He'll be sweet, very sweet.. then a few months later once he knew that the house was his home, he would become aggressive. We worked like crazy with him. Many times my parents threatened to sent him back to the shelter, but I constantly told them to just "hold on" that we could work with him. It payed off, he hasn't bit anyone in the family for over a year, but we have to be super careful around visitors or strangers. You gotta understand, though, that he was rescued from an abusive home that he had spent the first year of his life in.. he had a rough past and was never properly taught how to behaive and what was acceptable. Dogs like this just require understanding owners that are willing to put forth time and effort to break their habits.

Skylar(husky/GSD mix), on the other hand, was adopted, and he is the most loveable thing. 60+ lbs of pure love! He hasn't bitten a soul and has only growled once, and that was when I had taken him on a walk late at night and he had spotted a suspicious looking man. When visitors come, he doesn't even bark, and instead, greets with with big wet kisses^^. He knows the command "give me a hug!", and he'll raise up and put his paws around your neck and give you more kisses. Really, you couldn't ask for a sweeter dog.

I agree with what was mentioned, about talking so someone who is fostering a dog. They know all about that dog and can tell you what they're afraid of and how they act once they're accustomed to an environment.
I find that adopting a dog is a very rewarding thing! With more talking to your mum, I'm sure her mind can be changed. =)