In most cases when you open your door to the police they must ask permission to enter. They can't just barge in whether it's the front door or the garage door. This officer wasn't chasing anyone and the garage door was opened voluntarily. After determining who was the person who lived at that address the officer should've ask him outside to discuss a noise complaint (aka misdemeanor, ...at 6pm ???!!!) not invite himself inside...(4th amendment I think). And it is a violation of the OP's 1st amendment rights for the police to issue a fine for a noise complaint when the noisemakers (amps) were all turned off and the OP was only moving his fingers on the fretboard of an unamplified bass guitar. The OP's bandmates are credible witnesses. He should fight the fine. Some cops just hate to leave Dunkin'
A noise complaint is an infraction. LE has the authority to investigate a crime and they may enter a garage (in some cases) to do so. LE does NOT have to of been personally witness to an infraction. He was responding to a credible complaint by a citizen.
The OP acted incorrectly and by his obvious posts his attitude caused much of the problem. A simple "I'm sorry we will turn it down" would be the correct and proper response. But then, there would not be a thread.