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It's not based on trust, but verification by replication. The closest description is perhaps the security adage, "trust, but verify".

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So you trust that a conspiracy is less likely than people just replicating and getting the same results (within tolerance).

If you are unsure you can convince yourself by replicating and then others can trust easier because you're probably not part of a conspiracy.

But it's all based on trust in the end. Again, no _one_ replicates everything.

I don't trust that a conspiracy is less likely, I infer that due to logical arguments of parsimony (see Solomonoff induction), and then I verify that such a conspiracy didn't take place to the best of my ability.

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