Yes, that makes sense - even if mine is a better description of usage, from the standpoint of someone categorizing beliefs, I imagine yours would be the better metric.

It also has the advantage of making it clear that the chance that the statement is accurate is dependent on the competence of the person making the statement - people who are more intelligent and/or have more experience in the relevant domain will consider more, and more accurate, evidence to be readily available, and may have better intuitions, even if they are sticking to system 1 thought.

ETA: I'm not sure the caveat is required for "obviously false", for two reasons.

I suppose they don't need different wordings, but they do feel like different concepts to me. *shrug* (As I've mentioned elsewhere, I don't think in words. This is not an uncommon side-effect of that.)