I don't get it, how did they think this would go down? It's not like they aren't all really well recognized in the NCR to start with. Vance is a serial adulterer who basically just undermined the entire OP Honor program while abusing his authority over an extended period of time having inappropriate personal relationships with a subordinate. How else did they think it would be taken when they are publically hanging out with him? Even if the investigation doesn't find anything criminal, there is more than enough for pretty much anyone in uniform to be drummed out under an AR.
If he's your winger just have him over for a bbq or something. They are public figures, subject to public scrutiny. This send a message of public support for Vance, and just further reinforces the perception (reality?) that the GOFOs are a weird inner circle that are detached from reality. I don't get it. These are really smart people, and have been managing their public image for years.