Is it possible they're getting bad legal advice and the immigration cops were correct they really do need a visa?

Perhaps this problem would be solved if they got the correct visa. The law is very clear if you are band that routinely gets paid to perform, you must get a P-1 visa. It doesn't matter if you are getting paid for this performance, what matters is if you normally get paid. The reason for this is simple, many bands come to the US and claim they are not getting paid for performances when they in fact are.