IMO, the key word above is
company, as in "private employer." They can't just raise taxes on everyone to shore up their pension fund -- and if they have strong competition, they can't shore it up through pricing power, either. They either go under, freeze their pensions, or freeze their pensions and then go under.
As for SS, it will be around, but whether the payouts will decrease or the rules for eligibility change remain to be seen. One side benefit of my 401K's meltdown is that I feel a lot less likely to be means-tested out of SS benefits. Glass half-full.