sure, but we all hold crazy beliefs and bad opinions, not just a decent chunk of us. the amazing thing is that if, instead of trying to convince each other so hard, we averaged all our opinions together, we’d be collectively right much more than would seem possible. politics literally opposes this astonishing natural phenomenon. politics and ego are the enemy, not the wrongness that pervades the opinions of individuals.
I don’t think any of them are reliable enough to cite, on their name alone, as the foundation for a logical argument where “because X said so” is treated as absolute ground truth. That’s the essence of the “appeal to authority” logical fallacy.
Are they trustworthy enough to modify behavior in ways that appear proportionate to the risk when they make an recommendation and show their reasoning and whatever data they have? Yes, of course, but that’s no longer based on their name/reputation alone and, because it’s only a temporary behavior change, it has a much lower standard of proof.
Government authorities don't always convey scientific information, so you shouldn't trust them without question. I think the CDC has enough bodies in their basement that they need to account to any trust issues. That doesn't mean they will always lie to you, but you have to get secondary sources if you are critical.
And no, it isn't true what you say about the fallacy. It remains a fallacy if the only argument for a statement is authority of course.
[0]: https://en.wikipedia.org/wiki/Argument_from_authority