One has nothing to do with the other.

If they haven't paid you and you happen to own and operate it, just turn it off completely, there is no professional middle ground.

If a mechanic fixes your car and you don't pay them, in many places have have the right to seize your car until you pay. But they do not have the right to tamper with your brakes or spray paint "pay me" on your windshield.

Instead of being "stiffed", it is far more likely there is some degree of nuance. I'm sure if you called the market they would give their side of the story, and it would be something different than "we just took his services and didn't pay".

The problem here is the dispute that's occurring is being settled through taking the client's website hostage. That's ridiculously unprofessional.