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How is "a testing procedure is valid" defined?

For example, in Wikipedia

Fisher's exact test is a statistical significance test used in the analysis of contingency tables. Although in practice it is employed when sample sizes are small, it is valid for all sample sizes.

Thanks and regards!

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(Moving my comment to an answer so the question doesn't stay unanswered.)

I don't think the intend the word in a statistically technical sense.

I think they simply mean that the procedure works as a formal test at large sample sizes rather than being exclusively a small-sample test.

There's nothing about the way the test is constructed that assumes a particular sample size.

I suppose you could interpret it to mean something formal -- that they're claiming it has (no more than) the nominal type I error rate -- but I don't think they actually meant that.

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