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."
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."