Is ‘Trust-but-verify’ a frequently quoted word?

I came across a phrase ‘Trust-but-verify moment’ in the following sentence of Washington Post article yesterday. My interpretation of this phrase is ‘I trust you (and you’ve said), but now it’s the time you have to prove what you have committed to me.’ Is my understanding right? Is ‘Trust-but-verify’ a frequently used phrase? If so, why it is shown in Italic form in this particular quote?

Senate Minority Leader Mitch McConnell vowed that the Senate will vote on a repeal of the national health care overhaul, following the House's passage of repeal legislation last week. "I assure you we'll have a vote," McConnell said, adding that "it's very hard to deny people votes in the Senate." McConnell said that Obama has moved toward the center recently and said the president is now in "a kind of *a trust-but-verify*moment."

Solution 1:

Reagan was using the phrase because it is a common Russian expression. Доверяй, но проверяй. It's a contradiction, so to my ears, it sounds like "I don't trust you (but I don't want to say that so directly)"

Solution 2:

It's frequently used in political parlance thanks to President Ronald Reagan.

http://en.wikipedia.org/wiki/Trust,_but_verify

The basic meaning is "Make your plans based on the assumption that the other party spoke truly, but don't rely solely on their word."

Solution 3:

I always interpret it more or less as one of my favorite authors, Robert Heinlein used to put it (he stole it from somebody else IRRC), "trust everybody in the game, but always cut the cards."

In other words, it's good to trust people, but it's also good to make a habit of mitigating the risks of trusting - by, for example, cutting the cards.