What does Rick Perry’s “God uses broken people to reach a broken world" mean?

In the New York Times article of September 17 titled “Egghead and Blockheads,” Maureen Dowd introduces that GOP Presidential candidate, Rick Perry made light of his bad grades at Texas A&M in his speech to students of Liberty University in Lynchburg, Va.

Aside Perry’s acknowledgement that he ‘struggled with college, Dowd quotes Richard Oppel’s testimony that Perry’s D’s include Chemistry, the principles of economics, Shakespeare, Feeds & Feeding, Veterinary anatomy and Meat, plus C in Gym and one F in courses.

Dowd continues:

"It’s enough to make you long for W.’s Gentleman’s C’s. At least he was a mediocre student at Yale. - - -Perry told the students, “God uses broken people to reach a broken world.” What does that even mean?"

It is a great challenge for a foreign English learner to try to understand the line that even a reputed NYT columnist isn’t sure of. But I don’t think the America’s promising Presidential candidate spoke Greek to the university students.

My guess of Perry’s line, “God uses broken people to reach a broken world,” means that "the stressed country at the difficult time requires the ‘square-shouldered’ (cowboy type) brave leader who was hammered out of struggles (from collegehood) rather than an intellectual but Hamlet-type indecisive leader who kept being alpha plus at college." But I'm not sure at all. What is the correct interpretation of the “God uses broken people” line?

By the way, what is W in "W.’s Gentleman’s C’s."

For reference: In the Bible's New Testament, Jesus is said to have come into this world for sinners. (1 Timothy 1:15) In addition, there are several stories in the Bible in which Jesus uses "broken" or suffering people to do big things, i.e. Peter and Mary.

That said, it seems Perry is loosely saying that he made personal mistakes but that doesn't mean he can't do great things. Overanalyzing the words of politicians is a slippery slope. (For the record: I think Dowd knows full well what Perry meant.)

"W" is a reference to George W. Bush, distinguishing him from his father, George Herbert Walker Bush. His family is reported to have called him "W" as a child. Maureen Dowd uses it as an insult.

The line is from the Moses and David of Scripture, according to an online article in America Today, meaning that "He [God] does not require perfect people to execute his perfect plan", as quoted by Perry earlier in his speech. I believe the term broken people should be taken in that context, at least.

Perry's comment is that people in general are so imperfect that another "imperfect" person might understand them better than someone who "sailed through" with few blemishes.

At one job, one of the better supervisors I knew had taken about twice as long as normal to get to that level. He had made "every" mistake on the "way up," which is to say that he had more experience than others at fixing them.