Barret is not part of the SGC chain of command but they have occasional overlap. He probably did do the orientation check for mind control. Remember, the SGC has an actual, working lie detector, and it can pick up brainwashing.
Keep in mind up to this point, he's been competent, helpful, and has saved SG-1's ass multiple times. He also cleared the slime out of the NID.
You're completely right about the SGC making wrong decisions though. It sucks that the one person who called them on their poo was a mustache twirling villain.
Ronald D Moore likes to use this as a device in his writing, having opposition show up and call the main cast out on their poo. Sadly, he also likes to go with the villain route.
I know the writers tried to avoid writing themselves into a corner, like not letting the SGC have a sarcophagus despite the SGC repeatedly capturing and destroying Hatak class vessels, but they hand the idiot ball around a bit too freely.
I do like when Jackson is wrong and gets petulant, I feel like maybe that's the writers taking potshots at shanks.