If this isn't a publicity stunt, then the BBC has no idea how to handle the situation, or deal with high-profile talent. This should have been resolved internally, quietly, with no fuss, and without suspending the world's most celebrated show. Sure, Clarkson acted like a pillock, but come on, high-profile celebrities often act like pillocks and as a producer or television director it is your job to make sure that the whole show keeps going regardless. Instead, we have episodes suspended on a whim, dirty laundry being aired out in public, and a whole bunch of irritated viewers who just want their show back.
This is very unprofessional management on behalf of the BBC, and IMO the people responsible should be fired immediately.