What purpose are you after with this query? It sounds dangerously much like a semantic discussion, though I may be failing to see something obvious.

Fair question, I should've gotten this clear in my mind before I wrote. My observation is that there are people who reason effectively given their limited computation power and others who do not (hence the existence of this blog), and my question is by what criteria we can distinguish them given that the Bayesian definition of rationality seems to falter here.

If somebody points out the correct way to interpret some piece of evidence, then that correct way of interpreting it is information. Procedural knowledge is knowledge, just as much as declarative.

I would agree except that this seems to imply that probabilities generated by a random number generator should be considered rational since it "lacks" the procedural knowledge to do otherwise. This is not just semantics because we perceive a real performance difference between a random number generator and a program that multiplies out likelihoods and priors, and we would like to understand the nature of that difference.