What laws exist and what laws are enforced are two separate questions. It is a very minor inconvenience and expense to register a dinghy with the state. It one less thing that local authorities can bother you about. Besides, labeling your dinghy "Tender to" advertises that no one is likely aboard your boat when the dinghy is tied to the dock.All states have that it's called the Fourth Amendment to the U.S. Constitution, and it protects people from unreasonable searches and seizures. What is "reasonable" may be debated but without probable cause your person, home, car, boat cannot be searched.
As for the Fourth Amendment, writing a ticket for an unregistered dinghy is hardly a violation of the unreasonable search and seizure. The registration numbers must be displayed and visible.
Also, the Fourth Amendment does not apply to the CG. They have the right to board and inspect any vessel within the territorial waters of the US and they have right to board and inspect any US flagged vessel any where in the world.