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Notes -
I googled "positive claim" and one of the first relevant things that came up was Burden of Proof, which speaks as if positive claim means existential qualifier, For example, "there exists a teapot orbiting the Sun somewhere in the solar system." It contrasts that with a negative claim, which asserts the non-existence of something. Certainly, it is easier to prove a positive claim than a negative one.
The issue you're talking about seems to be more like "null hypothesis," which is definitely just cultural consensus and is essentially a rhetorical trick, and not very rigorous. When I took statistics class in school, I never liked null hypothesis as a concept, as I noticed that it didn't seem mathematical to me (although it was intuitive).
Science is not immune to this at least according to Yudkowsky. I've read attempts to formalize what burden of proof ought to be, and the ones that seem aesthetic to me are just having proof "in proportion to how complex the hypothesis is," which is in line with Occam (buzzword dump). This has the added benefit of ignoring the order that evidence is encountered.
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