Hello, Is it illegal to not promote someone because a fellow employee lied about you. My husband was trying to get promoted to supervisor at his work

The manager told him that he was not strong enough in a certain field. But did not tell him what in. They hired someone else. My husband found out by manager, that the persons place he wanted to take (He left for other job) Lied to manager and said he couldn''t do plumbing and got a lot of callbacks. This is not true. They hired him to do pluming work 3 years ago and he has not got any call backs. In fact my husband had done more than the supervisor himself. They took the word of an employee that didn''t want him to take his job so he discredited him. They did not confront my husband about what the other guy told them.. Oh the manager has only been at job for about 30 days. How can she judge him without being in the field with him or take the word at a jealous employee. This is an apartment complex and is in Lou, KY and the job he is wanting was maintenance supervisor and Manager is over the whole thing. Please answer this question because he needs to know what his rights are.