The are legal methods to have live rock in your aquarium - nodea's mentioned one. Conceivably, you could also collect trash (bottles, cans, snorkels, etc) with coralline algae on it and use it to seed your tank. There are also plenty of coral chunks that wash up on shore and are fresh enough to be useful in aquariums.
The "no live rock" rule is designed to prevent people from exporting live rock commercially. This IMO is a very destructive activity and I'm glad people aren't allowed to do it. In reality, though, nobody cares much about our personal aquariums and there are no "live rock police" who will come to your house and interrogate you about the rocks in your tank. Most people just grab a couple rocks from the beach when setting up a new aquarium (not that I'm advocating this).
Despite the regulations against coral and live rock, I think Hawaii is a great place to have an aquarium. There's no need for temperature control and salt water is easy to get. Everything in my aquarium is self-caught; I've never bought a fish in my life and I can't imagine ever doing so. There are plenty of invertebrates available (feather dusters, zoos, algae, etc) to make a tank look good, so not being allowed to keep corals doesn't bother me.