I know a bit about At-will employment and as I am sure there is a catch-all clause in their contract, A&E can only fire Phil if he does something they don’t like on the set or at a company function. Me thinks that’s why he was put on “hiatus” instead of fired. Once the lawyers form an opinion on whether or not he can be fired is when they will make their final decision. To my knowledge, in an at-will contract agreement, the company cannot terminate the contract for something that a contractor does away from the business that is not illegal. You can be fired for any reason, true, but then legally you can sue the company for lost wages, etc.
Merely noting that it is assuredly within their constitutional rights -- if it is contractually allowed, of course -- to "suspend" him.
It's amusing that, in order to serve the politically correct PR agenda, A&E now finds themselves caught between a.) the agenda and b.) their audience and profit.