His employer should be judging his work performance and character based on what they see at work.
They do have a right to fire him for whatever reason they want. I'm not claiming that. I just don't think it's right for them to fire him for anything beyond his work performance.
I don't think it's right for an employer to judge someone's character based on one act. What if this guy is a perfectly nice person and good worker at every other time (every day) his employer sees him and the only time he's seen him be an @ss is on this Youtube video? Why should the employer make a judgement on this man's character based on this one negative act rather than the cumulative history of all the positive acts the employer has actually witnessed.
But actually, I don't think that's even relevant. I think people should be allowed to continue at their jobs or be fired based on their work performance not on what they're doing in every other minute of their lives.
Jeeze! Talk about giving your blood, sweat and tears to the job! That's nothing. This would be your whole life.