you end up observing the outputs of models, as suggested in the original post.

I agree with pragmatist (the OP) that this is a problem for the correspondence theory of truth.

What is it that makes their accumulated knowledge worthy of being relied upon ?

Usefulness? Just don't say "experimental evidence". Don't oversimplify epistemic justification. There are many aspects - how well knowledge fits with existing models, with observations, what is it's predictive power, what is it's instrumental value (does it help to achieve one's goals) etc. For example, we don't have any experimental evidence that smoking causes cancer in humans, but we nevertheless believe that is does. The power of Bayesian approach is in the mechanism to fuse together all these different forms of evidence and to arrive at a single posterior probability.