A universal reasoner is allowed to use an intuition "because it works." They only take on extra obligations once that intuition reflects more facts about the world which can't be cashed out as predictions that can be confirmed on the same historical data that led us to trust the intuition.
For example, you have an extra obligation if Ramanujan has some intuition about why theorem X is true, you come to trust such intuitions by verifying them against proof of X, but the same intuitions also suggest a bunch of other facts which you can't verify.
In that case, you can still try to be a straightforward Bayesian about it, and say "our intuition supports the general claim that process P outputs true statements;" you can then apply that regularity to trust P on some new claim even if it's not the kind of claim you could verify, as long as "P outputs true statements" had a higher prior than "P outputs true statements just in the cases I can check." That's an argument that someone can give to support a conclusion, and "does process P output true statements historically?" is a subquestion you can ask during amplification.
The problem becomes hard when there are further facts that can't be supported by this Bayesian reasoning (and therefore might undermine it). E.g. you have a problem if process P is itself a consequentialist, who outputs true statements in order to earn your trust but will eventually exploit that trust for their own advantage. In this case, the problem is that there is something going on internally inside process P that isn't surfaced by P's output. Epistemically dominating P requires knowing about that.
See the second and third examples in the post introducing ascription universality. There is definitely a lot of fuzziness here and it seems like one of the most important places to tighten up the definition / one of the big research questions for whether ascription universality is possible.