I don't think the two examples you gave are technically that different. Someone giving an "intuitive" answer to the diagnostic question is basically ignoring half the data; likewise, someone looking for answer to P=NP using a popularity survey is ignoring all other data (e.g. the actual math).
The difference is whether you know what data you are basing your evaluation on and whether you know you have ignored some. When you can correctly state what your probability is conditional on, you are presenting evidence.
"I don't know of any unifying psychological theory that explains our problem with trivial inconveniences."
I suspect it is simply the combination of uncertain outcome and an opportunity cost. If I'm surfing the web and meet a wall, why would I go through even a trivial effort, when I can just hit back and click the next link? Perhaps most don't expect higher utility from reading a blocked page than another one.
I'm late to the thread, but I just had to leave a few thoughts.
Firstly, a well written post and I've thought about something similar too, as I suspect many have. I look forward to reading the Tegmark paper, which I have not yet done.
At least a couple of commenters opposed the jump from one to n to zero simulations, but I find it very intuitive. One can think about it like this: Suppose there is a non-iterative non-recursive formula for calculating the state of a deterministic universe at time t. This is analogous to having a digit extraction formula for pi. The simulation can then be stopped, rewound of forwarded at will, without any change to the actual results of the simulation. Someone inside the simulation would still exist as if the simulation had been played out in order.
The idea of universes as purely mathematical objects is also rather natural. If the state of the universe (including the laws governing it) can be encoded in numbers, it can be equivalently encoded in a single set. Then all possible universes are trivially contained in the universal set.
Where this whole idea begins to break down (or at least becomes non-trivial) is with non-deterministic universes. The result of such a simulation by definition depends on the machine/RNG running it, so they do not similarly exist as a sequence of states that could be navigated at will. Ours seems to be such a universe... Even in a non-deterministic universe each state would exist as a mathematical object, so maybe I just haven't thought about this enough.