Correct, you don’t have to be online for the Purge to happen to you. The server setting that controls it is inadequately documented and a source of confusion.
Here’s an explanation I posted once and I tend to link to it so I don’t have to keep copying it:
That setting is set to 0 on official servers, so that’s why you don’t have to be online for a Purge to happen to you, but someone has to be online on the server for the Purge to happen at all.