Earlier quoted context omitted.
does it ? > Reagan used the phrase to emphasize "the extensive verification procedures that would enable both sides to monitor compliance with the treaty"
But you have to look at why he used that particular phrasing–a clever bit of wordplay to quickly get the idea across to Russians in familiar terms. It's a Russian figure of speech in the first place.
“Wordplay” is too generous IMO. The original russian proverb is also double speak, as we would say now.
It’s obvious when applied to trivial situations:
“I trust my wife, but I take the time to verify her phone every night and check the private eye report of her day”
We wouldn’t call that “trust”, pretty much the opposite