It's possible to trust (or have faith) in my car being able to drive another 50k miles without breaking down. But if I bring it to a mechanic to have the car inspected just in case, does that mean I never had trust/faith in the car to begin with?
"I trust my coworkers write good code, but I verify with code reviews" -- doing code reviews doesn't mean you don't trust your coworker.
Yet another way to look at it: people can say things they believe to be true but are actually false (which isn't lying). When that happens, you can successfully trust someone in the sense that they're not lying to you, but the absence of a lie doesn't guarantee a truth, so verifying what you trust to be true doesn't invalidate your trust.
We're getting into the definition of trust, but to me trust means exactly "I don't need to verify".
If I say I trust you to write correct code, I don't mean "I'm sure your mistakes won't be intentional", I mean "I'm sure you won't have mistakes". If I need to check your code for mistakes, I don't trust you to write correct code.
I don't know anyone who will hear "I trust you to write correct code, now let me make sure it's correct" and think "yes, this sentence makes sense".
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.
It's a matter of degrees. Absolute trust is a rare thing, but people have given examples of relative trust. Your car won't break down and you can trust it with your kids' life, almost never challenging its trustworthiness, but still you can do checkups or inspections, because some of the bult-in redundancies might be strained. Trusting aircraft but still doing inspections. Trusting your colleagues to do their best but still doing reviews because every fucks up once in a while.
The idea of trusting a next-token-predictor (jesting here) is akin to trusting your System 1 - there's a degree to find where you force yourself to enable System 2 and correct biases.
