Not sure why there would be an expectation that Priority Security = PreCheck? Every airline offers some variation of this (SkyPriority, First Class Security Line etc.), while PreCheck is a TSA-run program where TSA calls the shots on who gets access.

You may randomly get it on occasion even without registering for the program, although TSA has been reducing the slots for that pretty significantly, but that could happen regardless of if you were in Basic Economy on your first ever flight or Mint as a Mosaic 3.