More fridge logic:

The Dark Mark. Everything we know about it is that there are very specific restrictions on how the bearer can conceal or display it, and what they can say about it.

Snape, who is subject to the restrictions about what he can say about it, provided information (consistent with all previous information, all of which he is well aware) that Harry, by describing how to use the restrictions on speech to identify bearers, removed those restrictions. Snape then allegedly described the restrictions, and the description he gave is roughly the stupidest possible one that is consistent with all available data.

Which is more likely, that the Dark Lord created a mark that prevents people from saying what it does unless they are told that they will be asked to say what it does, and in that one case ceases all operation... or a Dark Mark that has the restriction "Provide as little true information as possible about the nature of the Dark Mark.", which would force a response identical to the one received.

How does one perform a Bayesian update where A is "The phenomenon produces evidence B in such a way as to minimize the value of P(B|A)/P(B)"?