As you say, this isn't quite self-trust. Another natural move is to relax the criterion of self-trust away from "it proves itself consistent" (impossible by incompleteness) towards "it assigns high probability that it has good beliefs". (Formalizations of this are in the paper.)
> At the moment I'm just confused what the problem is
In short, it would be nice to have a model of "good reasoning under deductive limitation", where "good reasoning" means something like "has accurate beliefs about all questions of interest" (for example, facts about the outputs of long-running computations), and where "deductive limitation" rules out the reasoning process "just wait for your theorem prover to decide the question".
Examples of long-running computations that are hard to compute exactly, but that we can sometimes still have reasonable beliefs about: optimal moves in chess, go, etc.; the accuracy of some ML system after a given training regimen; a weather-forecasting program that runs a gigantic series of simulations; and so on.