There is a hole in your Cost Pass Trough argument.
On the contrary the hole is in your choice of example. BA has already decided that it can't pass the cost of it's pension arrangements onto customers and taken far more drastic steps than NATS to reduce its pension costs.
With regard to the fines if you look at the BA accounts you'll see that BA has made provision in its accounts for those and has effectively reduced its profit by that amount. Technically that means the shareholders have taken that hit because it reduces the amount available for dividends and reduces the amount re-invested and re-investment is usually to the benefit of shareholders. You are right of course that ultimately anything BA pays comes from money paid by its customers and they could put up fares to recover that lost money. Whether or not they do will depend upon how cost sensitive their ticket sales are.
BA is considerably larger than NATS and can absorb much larger financial shocks without recourse to its shareholders. The two companies are far from comparable in many ways.
The Airline Group is a shareholder in a limited company just as I and many others are. If we are going to worry about the provenence of shareholders presumably we'll have to assess all members of staff to decide whether they are right and proper to hold shares.
They caused the problem. They can fix it
Even if that were true nobody has yet explained quite where the money to fix it would come from. There is no pot of cash and the regulator won't increase the charges so how exactly do you expect it to be fixed ?