No, what they are confusing is that the former TW f/as (possibly others as well) who were eligible for their PBGC-administered pension from TWA were able to start drawing that pension while on furlough from AA, and continue to draw it even if they have been recalled. Two different companies. Two different pension plans. And, the paying company (TWA) no longer exists.
If you are an AA employee, you may not draw a pension from AA unless you retire from AA.
Yes, you can draw Social Security and continue to work, but SS is not company-specific as far as the payment of benefits like a DB pension plan is. I am already drawing Social Security and working full-time. In fact, my SS payment has already increased a little for the additional contributions made after I started drawing.