Old-school PSTN folks looked at XKCD 705 and chuckled. Late to the party, pal.
The telephone network was designed from the ground up to be completely independent of _everything_ except fuel deliveries. If grid power is up, that's convenient, but it's totally not required.
In many places, that's because telegraph and telephone lines got there before the power grid did. Lines running along railroads connected communities that had no centralized power generation. Delco-light plants at individual farms might be the only electric power for miles, aside from the communications lines themselves. Even if the only phone was at the rail depot, it still had to power itself somehow. As those communities sprouted their own telephone offices and subscriber lines branching throughout town, the office had its own batteries for primary power, and eventually generators to recharge them. (Telegraph networks largely ran from just batteries, recharged chemically rather than with generators, for years.)
Fast-forward a century and there was just never a need to depend on anything else. As long as the diesel bowser can get down the driveway, the office can run indefinitely.
Among old AT&T/Bell/WECo hands, the devotion to reliable service goes far beyond fanatical. Many offices built during the cold-war have showers in the basement and a room of shelf-stable food, though these are no longer maintained. The expectation was that whoever was in the office when the bombs dropped, would keep things running as long as they could. And when they couldn't anymore, well, there was probably nobody left to call anyway.