I’m a switch tech, and lemme tell ya, it takes A LOT to crash a system..
Yep. Used to work for Ma Bell. They’ve been building switches for so long (and you know they installed top of the line equipment for the gooberment), that if it is true, that’s one hell of a volume.
There are a fixed number of lines going into and out of every phone system. Based on 25 years experience with these systems, there are only four plausible explanations: 1) As configured, the phone system is failing before all trunks are busy which is a design issue. 2) The system failed for a reason unrelated to call volume, i.e. it's a coincidence. 3) The system recording voice mails ran out of disk space. 4) They intentionally shut the incoming trunks down.