The provision you mention is part of the "Uniform Commercial Code," which is in the USC (United States Code), and has, I believe, been adopted by every state.
It does not apply to service contracts, etc. This is a situation where you need to know the exact purpose and wording of a rule; folks are always mis-applying this one.
If you're in a situation where you have performed work, and the customer does not wish to pay, you will have to exercise your usual remedies- Small Claims court, Lien, etc. At that point the customer will have to justify his action. He may try to cite this part of the USC. That's where you have to be prepared to rebut him.