Pretty easy. Retard gets weird call; retard's phone shows Patrick's number on the caller ID; retard phones Patrick back and spills the beans.
Even if the retard is not someone who knows Patrick and therefore has no specific desire to clue Patrick in on the incident, you'd be surprised how many people are dumb enough to call any old number right back, thinking they'll get even over the telephone and set that scammer straight.
I can actually believe a stunt like this is a plausible thing to happen. Spoofing your number is apparently quite easy if you know what you're doing. Scammers and spammers aside, prank call podcast hosts have been openly doing it for years. (Although the word of late is that spoofing might soon become impracticable because voip providers are cracking down on it.)
What Pat has no way of knowing is who the culprit is. Like with the swattings, he automatically blames the Stlaker Cult, but it could just as easily be any old rando.
Not to worry, I'm sure his contacts at the FBI will have those calls traced in no time.