I watched just a few seconds of the videos, and each seemed to be more interested in telling one side of a story instead of reporting all of the facts. That said, here's what the PBGC does:
The PBGC (Pension Benefits Guaranty Corporation) are to pension plans what the FDIC (Federal Deposit Insurance Corporation) is to bank deposits. You may remember the tag line at the end of bank commercials, "Member FDIC," meaning that your deposits were insured by a government entity in the event the bank went belly up.
Defined benefits pension plans are what we think of as the classic pension plan people receive after they retire. It's a guaranteed $___ per month for life, and many times a surviving spouse will receive those benefits upon the retiree's death. During employment, employee and employer each contribute to the worker's account. All plans for an employer are managed by an administrator - sometimes a trust company, investment company, actuary, or even an accountant in small instances. They cannot be the plan sponsor (employer) - they are supposed to be an independent fiduciary.
The PBGC oversees these plans, and require sponsors to pay annual premiums to the PBGC that insure the underlying retirement accounts. Joining them in oversight is the IRS and US Department of Labor. All wield big sticks. My company - founded by my grandfather - had such a plan, and those three agencies would threaten me under pain of death if our plan was underfunded. It never was.
What is that - "underfunded?" When assets in the plan do not equal or exceed the plan's liabilities, accounting for a reasonable rate of return. In my case they never did - we were overfunded. In AMR's case, the plan is grossly underfunded, and they have been under pressure for years to make up the deficiency. If they didn't, and went into bankruptcy with an underfunded plan, the PBGC would have to make up the shortfall to retirees, but never all of the shortfall. That is what you see today. Many cities and states also have defined benefits pension plans, and many are underfunded. How do officials get away with that? They tell PBGC auditors that they expect an annual plan ROI of __% which will support the underlying liability. Unfortunately, the ROI is always greater than anyone has ever achieved in history, including Warren Buffet. They're whistling past the graveyard, but by the time the train wreck occurs (plan payments to retirees exceeds plan income and it collapses), the officials have moved on.
Back to AMR - their plan is underfunded, they asked Congress for a temporary moratorium on plan contributions during recent difficult times (in the past couple of years - I'm not exactly sure when), and that was granted on the condition that the suspended contributions be made up. They never made up the shortfall and went into bankruptcy. Because AMR and pension administrators lied to Congress and the PBGC is why neither is sympathetic to their plight.
Yaaa-up! Dirty mouth an all. Then saying, "We aint eat'n noth'in kid! Mind yo bizz."