The issue here is that the only value of the adage is in the sleight of hand it lets you perform. If someone asks "don't you trust me?" (ie "do you have to verify what I do/say?"), you can say "trust, but verify!", and kind of make it sound like you do trust them, but also you don't really.
The adage doesn't work under any definition of trust other than the one it's conflicting with itself about.
I think I just provided an example where it makes sense.
Specifically: I have confidence in your ability to execute on this task, but I want to check to make sure that everything is correct before we finalize.
The adage doesn't work under any definition of trust other than the one it's conflicting with itself about.