I'm sorry, but I completely disagree with your sentiment. If there was a problem with your line that caused a 911 call to be made, you cannot fault the police with following protocol. How can they know that it was a problem with your line that caused the call to take place? How are they to know that you didn't do something to your girlfriend that caused her to call 911, only for you to hang up the phone before she could do or say anything? In that case, it is perfectly logical that they would conduct a search of your apartment in order to ensure that you didn't do something further to her because she tried to call for help.
I mean, why should the police believe you that there was nothing wrong? Because you said so? Sorry, not a good enough reason. Had something actually happened, and they simply left because you said there was some kind of mistake, and a body was later found, the public outcry would have been enormous.
The police just can't win. We expect them to do their jobs, but when they do do their jobs, people get angry because they might be a bit inconvenienced. I just don't understand it.