If we're talking about what's best for the company, then only the relevance of the facts should matter.

Up to a certain point, of course. But all this talk of how to deliver information so the recipient feels nice about receiving bad feedback (shit sandwiches and such) shouldn't matter.

To a point. While any given speaker should always endeavor to deliver their point for maximum effectiveness, by the same token, discounting or outright ignoring feedback simply because it's worded poorly or timed poorly is like rejecting your paycheck because it's printed on green paper instead of white. The money is still there, and it's still usable, and you're only hurting yourself because it didn't come how you thought it should.

Frankly, as someone who leads a team myself, yeah I've had to take colleagues aside and say "this isn't how we do things" but I certainly wouldn't just bin their entire point without consideration to save "face."