When they're talking about the PBGC, that's private sector. In many cases, management (to avoid a strike) and unions officials (to keep their positions) essentially colluded to make promises to union members they new/suspected they wouldn't be able to keep down the road. By the time those pension plans came due, it would be someone else's problem.
I don't see why it should be ordinary taxpayers, most of whom don't have a pension of their own, to be on the hook for those promises.