Obviously, but the idea that we can only have one standard or the other seems like a false dichotomy. Maybe we should be looking at how to take a more Bayesian approach to legal decision-making.

Sure. The legal system does sort of support that - the standard of evidence in a criminal trial is a lot higher than in a civil suit. It's quite possible to be in a situation where for some reason the government cannot punish you for a crime (maybe failure to prove beyond a reasonable doubt, maybe expiry of the statute of limitations, which is also a check on the government's power), but someone can publish that you have committed a crime, and another suit will decide that what they've said is true enough to avoid them having libeled you. Or they can find you in breach of a contract where you said you wouldn't do what you did, etc.

(My understanding is that this is basically why you sometimes see contracts banning illegal behavior. It's hard to prove illegal behavior to the extent required to throw you in prison, and that's a good thing, but it's easier to find you in breach of contract.)