Is it possible to dismiss a discharge from an employer for unintential harassment?

My brother got fired from his job only after three days employed for harassment. According to what his boss said was that a woman reported him for trying to "hit on her" When in truth all he was doing was trying to be friendly. He says all he asked her was if she had a boyfriend. While i know he is not single himself (he's been married for 3 years now) he does suffer from several social disorders. The victim in question was on a field interview and was considering not joining the company because of this occurrence, and if he was allowed to stay on there would be a risk of the company being sued. Was this handled correctly? Should he try to speak to the owner of the company over this matter and explain? And Is there anything he can do to get his job back or is it pretty much sealed? Personally, I think this was handled incorrectly and unfairly due to my brother's disorders. Any help or answers to this question would be appreciated.