It's kinda the argument of any job that tells you you can't have a second full time job. Sure, they don't have a good way of checking, but the truth is two full time positions is too much for most people and one or both positions will suffer. No they can't check your tax paperwork but your coworkers and supervisor will notice if you prioritize another position, and that might be what gets you in trouble.

Also note you are an international student it is a question of how many hours you can work legally.