I've seen those here in Alberta, but it's a bit more than an answering machine. Oddly enough in old radio documentation (mainly scanner books) it was called the P.E.R.I.L. System - I have no idea what the acronym stood for.
The "dispatcher" was most often a firefighter, medic, or even just a town clerk, with a portable radio. Dialing the "emergency number" just activated the inbound part of the phone patch for the repeater. Every little detail of the "911 call" could be heard, broadcast all over the land. Frequently the "dispatcher" would have to remind the caller that they were on a two-way radio, so they couldn't hear the caller while they (the dispatcher) was talking, so they had to hold their answers for when they heard the over-beep.
I won't delude myself that that kind of system has been eliminated from everywhere in Alberta, but all the places I know of near me dumped it many, many years ago. Just as well... here are some of the reasons things got weird:
- One town used the second ambulance crew (of 2) to answer the emergency phone. When both crews were on calls, whoever was the least busy ended up having to pick up the call. Yeah, while responding, or rendering patient care. Yeah.
- Another town used civilian dispatchers who were free to roam about town doing their business since they could activate the station tones from the keypad on their radios. It was not uncommon to hear "can you speak up, I'm in the hockey arena and it's hard to hear you" and things like that.
- One department I know of contracted to another department for this kind of dispatch service. The call (before 9-1-1 existed) was a ten-digit long-distance telephone call for the area's residents, to report an emergency. Consequently the reverse was also true - in order to set the subscribing department's pagers off, the dispatcher had to dial long distance. Like the other department, their dispatchers could roam. But this was before widespread use of cell phones, and definitely before department-issued phones. So the dispatcher would have to go to the dispatching agency's firehall to make the long-distance call, so they weren't having to make long-distance work calls on their own dime. It was a regular occurrence to have a time between the caller dialing the emergency number and the crews being paged out being on the order of 7 to 10 minutes.
The majority of Alberta is now covered by 9-1-1 and full-time paid dispatchers in a professional comm center. Even in volunteer departments that still have just a repeater and a phone patch, the dispatcher in the comm center just dials the phone patch up and alerts the crews from there.
Like what VE1SEF said, the biggest grief in Alberta has been convincing people to use their "emergency number", "municipal address", or however you want to name their new, uniformly-designed address created to locate them in the 9-1-1 system. Everyone from the elderly (who only remember being told that "the number on this paper is important, keep it by your phone") to the crusty old rancher ("I don't have an address, just tell them it's where the brown cows are") argue with calltakers all the time. To make matters worse, the old addressing format in Alberta rural areas (and in SK and MB as well) is a string of numbers that correspond to a square-mile parcel of land. People think that's sufficient to get an ambulance or fire truck to them. It's not. My house and 58 others in my community share the same "address" in this antiquated format. It might work if the house is on fire (just drive to the glow) but not if someone's having a cardiac episode....