That depends on the circumstances.
Aboard my ship, we had "Captain's Call" where the lowliest "deck ape" could, in front of the assembled ship's crew, ask and/or gripe directly to the CO about whatever problem was on his mind skipping his Petty Officer, his Chief, his Division Officer, his Department Head and the XO.
One question I remember was why the CO was allowed to do such and such with his wife when the ship was in port but E-Zeros were not. He replied that when he was at the bottom of the pecking order, he could not do that either but that there was nothing stopping any junior enlisted from putting in the work required to someday command their own ship at which time they would have similar privileges.
The CO had no obligation to hold Captain's Call and put himself in positions that even had him explaining why he could do such and such with his own wife. However, the CO voluntarily put himself in that position and he accepted the consequences.
Likewise, Rumsfeld voluntarily put himself in that position.
If a superior is not willing to get smacked with tough questions that did not march up their way up the chain of command, then they should not hold such events.
You may have had a localized policy at the discretion of your CO, but to extrapolate that to a public embarassment of the SoD is beyond the pale.
..and was not immediately broadcast to the whole world, including our enemies!!!!!!!!!!!!!!!!