Bank runs are a psychological phenomenon.

If you're looking at a bunch of companies you're invested in taking a 5, 10, whatever percent haircut on their deposits, it might be to your interest to take to the media and encourage everyone to panic, helping to create the very risk of contagion that you're talking about, to try to force the government's hand.

They are using their media influence to "threaten" a bank run. Aka, if you don't bail us out, then we might as well take the whole system with us.

No, this has the power to cause the fire to get much larger because the shout gets heard way outside the theater.