You'd imagine in this day and age Jamie's employment contract with Sky will have exit clauses to cover reputation in both directions.
Whether or not Sky chooses to exercise their right to early termination is another matter. Whilst to the Average Joe it might seem just, big business rarely is. He's an asset and he pulls in viewers, if they decide, in the balance, that this incident will be a detriment in viewing figures in the whole then he's gone but I'd expect they'll keep him on.
With regards the man filming, it will be interesting to see if it becomes a criminal/police matter.