It's really easy to fire someone in America. You just tell them "you're fired." In theory, employment is "at-will" meaning that as an employer, you can fire someone for any reason or no reason, and as an employee, you can quit for no reason, too.
Practically, though, there are a number of reasons it's illegal to fire someone, or there are implied contracts in things like all that paperwork you sign when you get a job, or racial discrimination, or sex discrimination, or a number of other things, and Ali would have lit up red lights on being a likely source of litigation. She's vindictive, crazy, and all kinds of other negative things.
They'd want to make sure they had a really good reason to fire her, one that she couldn't sue over.
Getting caught as a prostitute pretty much ended the debate. That had to have come as a relief for whoever already wanted to fire her.