Often we judge if somebody else is understanding something that we do not understand by whether the things they say in response to our questions are surprising.
When somebody understands it about as well as you do, the things they say about it will generally be fairly understandable and expected (as they mesh with your current insufficient level of understanding). But if they actually understand it and you don’t, then you should expect to be surprised by the things they say, since you couldn’t have produced those responses yourself or predicted them coming.
Q: “In this step of the proof, are they talking about extending the model or the language?”
A1: “They’re talking about extending the model. Look at the way that they worded the description of the extension in the previous step, it specifically describes adding a character to the model, not the language.”
A2: “No, they couldn’t be extending the model even though the wording suggests that, because then the proof wouldn’t even work; it’s required that we just change the language or else we end up working with a different model and failing to prove that the original model had the desired property. Also, it doesn’t even make sense to talk about adding a character to a model, the characters are a property of the language.”
Even with no context to judge whether the claims are true, I imagine that the second response feels much more convincing than the first, even though it’s probably less likely to be understood. The first is the type of response that is unsurprising and easy to see coming, and indicates only that the person is understanding the grammar of the English sentences they’re reading. It doesn’t strongly discriminate between a person that understands what’s going on and a person that doesn’t. The second is certainly surprising; it suggests that the person objects to the specific wording of the proof because of their understanding of the way it misrepresents the logical structure of the argument. They aren’t just comprehending the grammar, they are comprehending the actual content. Ordinarily, a person wouldn’t be able to off-the-cuff make up a response like that without actually understanding what’s going on.
This is a problem when people are good at saying surprising things without understanding. I’ve met a few people that are very good “contrarians”; they are good at coming up with strange and creative ways to say things that ultimately shed very little insight on the topic at hand. I often found myself in a weird position with such people where I feel like they understand the topic at hand better than me, and yet simultaneously I’m deeply suspicious of every word coming out of their mouth.