You're very close to the story. Pennzoil at one time advertised their oil as being made from paraffinic base stocks, which is an another name for alkane hydrocarbons. Paraffinic hydrocarbons can range from gases, to liquids, to solids at room temperature.
However, Billy Bob read the advertisement and exclaimed "Paraffin! Gadzooks! That's the stuff Erma uses to seal her jelly jars!"
This really got a lot of traction as multi-viscosity oils became prominent as most oils of that era has significant sludging issues. The average consumer found out his engine was sludged up and decided "Well it's no wonder, that **** Pennzoil has paraffin in it!".
Pennzoil never had paraffin waxes in the oil. And they never had more sludge issues than the other oils of the era. They were however one of the most popular brands at the time so if you had an engine with sludging issues there was a fair chance it was running Pennzoil. It was a case where someone took a small bit of information and ran with it beyond their understanding.