[SoftTalker]

That's only one possible meaning of the word "trust," i.e. a firm belief.

Trust can also mean leaving something in the care of another, and it can also mean relying on something in the future, neither of these precludes a need to verify.

Edit: jgalt212 says in another reply that it's also the English translation of a Russian idiom. Assuming that's true, that would make a lot of sense in this context, since the phrase was popularized by Reagan talking about nuclear arms agreements with the USSR. It would be just like him to turn a Russian phrase around on them. It's somewhat humorous, but also conveys "I know how you think, don't try to fool me."