Okay, so this is the video that anon was talking about, the clip in question is at about 23:21.
I do believe this is legit!! The video compiler's claim of finding it on the SP website in 2008ish makes sense to me as they did used to host odd clips and flash games among other things that you could not find anywhere else. It doesn't make sense for something like this to be "AI generated" and that is *definitely* Trey's voice acting for the male caller. The quality of the clip also matches that claim for me.
Here's a memory thing for me that may or may not be accurate, but I'm pretty sure that Trey (possibly Matt was also involved?) would do some radio skits that were either south park itself or just along that line of humor, my mom claims to have remembered hearing it on stations before (specifically she recalls the "o holy night" with the cattle prod being something that she also heard on the radio, not just in the episode). I wonder if there was something of that nature done on an actual broadcast as a sort of skit or prank, which the studio then animated and put on their website????? I could be completely wrong but that feels like something that would happen.
Either way, I don't think the clip is faked, just very obscure, and I would love to know the context for it.