"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.
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".
Or maybe the proverb needs to be rewritten as “feign trust and verify”
That's a bit wordy but I'm sure someone can come up with a pithy phrase to encapsulate the idea.
If you use the slightly weaker definition that trust means you have confidence in someone, then the adage makes sense.
The adage doesn't work under any definition of trust other than the one it's conflicting with itself about.
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 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.