It looks like it’s not true, though the confusion is understandable. “New Jersey” was not named as such until after Pennsylvania was founded. However, it was called East and West Jersey; West Jersey was sold to Quakers including William Penn. However, eventually East and West Jersey were united into New Jersey.
So Penn was co-owner of East Jersey, but that land was never part of Pennsylvania.
Reality Chuck got there first, but the answer is “No Way”.
as a kid growing up in New Jersey we learned about East and West Jersey, and about the settling of Pennsylvania by the Quakers. Never a hint of Pennsylvania being called part of New Jersey. And I never found anything like that when researching NJ colonial history.
I think “New Jersey” has just become the easy butt of the joke, mainly by NY celebs and comedians who see it as an easy way to get a laugh – nobody would admit to being from NJ, especially with those smelly refineries in Linden and Elizabeth.
So you could say anything about New Jersey, practically, and people will believe you.