I don't know whether this myth was ever true, but it certainly is not true today.
I have called 911 or its equivalent more than a dozen times on three continents. No magic helping people appear within five minutes. Or ten. Usually not twenty either. Sometimes not at all, even when they say they will come.
We pay fees for E911 service which includes location of cellular phones. But if you call 911 in Manhattan and tell them you are on 4th Street they will ask you if it's East or West 4th. They will even ask you this if you say you're on 3rd Avenue--an absurd question for a local resident but not for 911 dispatchers who are not locals and do not know local vernacular much less geography.
A few days ago the car I was in was robbed while we were driving in Chicago. I immediately called 911. They said they'd send someone so I told them where to find the driver. They called me back 20 minutes later and said they were not coming and that such a crime could be reported by phone only. The driver's phone had been stolen.
A fire alarm went off in a commercial building. I called 911. They didn't show up. Forty minutes later I called again. They sent the FD to my house. Not the fire.
911 is broken. Be prepared to take care of yourself.