It's not the Pig'n Whistle. It's not the other Pig'n Whistle. But it's a Pig'n Whistle. Perhaps it was connected to the famous P'n W in some way other than the owner figured the original was too dang far across the country to complain, but I don't know.

This site says the original's name was simply inspired by the logo, which showed a pig playing a whistle. Not to play Snopes without a license, but I think that's probably the origin on the name, and the stories inside the matchbook are bogus.