And you're right. But they have every right in the world to do that if they feel he's costing them money. Imus wasn't arrested or killed or sent to Siberia for what he said. He got suspended. That's it.
Sometimes we mistake the 1st Amendment's meaning and we think it gives anyone the right to say anything they want without consequences. But that's not what it says. All it says is that Congress shall make no law abridging freedom of speech. If I went up to my boss and told him he was a no-good, lying SOB I'd get fired from my job and I'd deserve it and he'd be within his rights to do so. But I couldn't be arrested for saying it. I'd just have to get another job. If Imus wants to sue his employer for suspending him, God bless him. He's got every right in the world to do so. He also has a right to quit his job and go elsewhere if he doesn't like it there.
His employer also has the right to take action against him if they feel he is hurting their business. The basic principle of a capitalistic society is to make as much money as you can within the bounds of the law. You don't have to lose money if you don't have to.