They aren't talking about something that tells you whether a statement is true or false, but something which you can present your line of reasoning to, and it will check that your reasoning doesn't include an invalid step, or a gap that would need to be filled in.
I've definitely had the experience of "I think this is a valid proof. I haven't seen it presented anywhere else, and I'm not super familiar with the subject matter. It feels a little socially awkward to ask someone to check if it is right", and I started trying to express it in Lean.
However, I found it difficult to get the implicit type parameters to work right, so I had trouble even formulating the claim in Lean. (the claim was a claim in category theory, and the category theory library for Lean has lots of implicit argument stuff, and probably shouldn't have been the first thing I tried to use Lean for. Also the claim I was trying to show is probably very simple for category theory people.)
I've definitely had the experience of "I think this is a valid proof. I haven't seen it presented anywhere else, and I'm not super familiar with the subject matter. It feels a little socially awkward to ask someone to check if it is right", and I started trying to express it in Lean.
However, I found it difficult to get the implicit type parameters to work right, so I had trouble even formulating the claim in Lean. (the claim was a claim in category theory, and the category theory library for Lean has lots of implicit argument stuff, and probably shouldn't have been the first thing I tried to use Lean for. Also the claim I was trying to show is probably very simple for category theory people.)