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Great example, Eliezer. 2 + 2 = 4. This is one of those rituals that scientists go through every time the analyze data. Do they sit down and prove 2 + 2 = 4? No, they don't. They stand on the shoulders of greater men (to use Newton's phrase I believe), and use their computers to move on. Requiring every working scientist to reexamine every assumption - is well, philosophical (which is fine) and uneconomical (which is less so).
I'm beginning to think that the blogger at hand doesn't understand science. Was there anything we could call science before peer review? Isn't science not only the repeatablility of the experiment but also the validity of its method? How do you know your experiment's method is valid? Isn't the majority of the method based on tried and true techniques learned in school, ie, tradition? Whenever a chemist uses a pipet load a chemical to into a test tube, how does he know it's the correct quantity? Etc, etc.
The criterion is too high. Too many of today's scientists -- personally, I bet, all of them -- would have to pack up their bags and go home if they couldn't hold any unprovable beliefs (as last year's Edge.org essays demonstrated, most people believe something they cannot prove). Certainly we'd have to discard Newton, Einstein, Godel from the pantheon for their metaphysics.
Why not let scientists believe whatever they want? Why worship the scientist as a perfect unbiased hero dredging against the sins of falseness? Seems too much to ask from a single human. And not very accurate: science is a social institution. It relies on convincing others that not only your interpretation of the data is correct but that your technique for getting the data is kosher and that you aren't outright making things up. There are checks and balances (even if fallible in the short-term) in science - but no scientist is an island of truth. That notion doesn't begin to make sense. There really wasn't much science until people wrote back and forth to each other asking "Can you confirm this?" and "Does this make sense?".
Mentioning Isaac Newton should itself disprove the current post's hypothesis - 90% of his writing was about alchemy and conspiracy theories and other beliefs even his contemporaries didn't bother with. We can only trust his good ideas because the good ideas were confirmed by others. That's the best we can ask scientists to do. Have ideas, throw them on the fire of like-minded folks, see what sticks. Likewise when Dawkins goes off about the psychology of religion - well, it's really opinion that wouldn't get (or hasn't been) published in a peer-reviewed journal. That's how we know not to take it too seriously. But we can still take his work on molecular biology seriously enough.
To expect a scientist to be statistically perfect in any sphere their mind wanders -- politics, religion, relationship with their spouse, child-rearing, literature,music, art -- is to ask them to be very, very quiet.