That roughly sums it all. My experience with the PMs there is they were always at meetings but nothing positive or productive came out of it and its final verdict is 99% the prerogative of the development teams to handle the problems themselves. Even if 1% successful was also only delaying the deadline. Those closer to the management ones will manage to wash everything off their hands and the teams below them will take the brunt of the blames.

Then the PM will miraculously be promoted in the next 1 or 2 promotion cycle.