I think this take is dangerously mistaken, in a similar way to standard “but sometimes the utility-maximizing move is to believe something false” takes.
According to me, the main problem with “sometimes the utility-maximizing move is to believe something false” is that, in practice, we live in a very hostile memetic environment. The memes around us are under intense competitive pressure, evolve very rapidly, and will exploit any hole in our epistemic armor. If one is willing to sometimes believe a thing for any reason other than “the thing is true”, one will quickly encounter parasitic memes trying to exploit that willingness—memes claiming that it is good/useful to believe X regardless of whether X is true, usually with the implicit claim that checking whether X is good/useful to believe would itself imply less belief in X and therefore be bad. Accepting beliefs for reasons other than the belief being true is like running Windows XP and connecting to the internet.
Your take has a similar problem, but at the group epistemic level, rather than the individual level. In a hostile memetic environment, it is extremely dangerous to accept any justification which grounds out in optics, consensus, legibility, etc. Parasitic memes can and do evolve to exploit that sort of loophole.
Good question. This is getting too far from the object level for me to think well, so let’s start with how I would think about the situation with Caroline. If I were in Austin’s shoes right now, I would (a) explicitly publicly declare that I was betting my own social capital on her, and (b) make sure to double-check what Caroline’s doing from time to time in order to protect my own social capital. And of course if she did go pull a fraud again under my watch, I’d take responsibility for that.
On reflection, that answer seems straightforwardly correct, but I haven’t thought about the right ways to generalize it.