I picked up my truck last Friday from the dealer after dealing with the same problems. They told me that GM had told them to change the starter and (I'm guessing) at least one battery cable. It was my salesman that told me, and not being a mechanic he phrased it as "the starter and something else with high resistance". That it why I'm guessing that what he was referring to was a cable since somebody else in this forum had a battery cable with high resistance changed as a result of this very issue.
It has been sub-zero overnight at least one if not two of the nights since I got the truck back, and the highest temp has been today at about 25. The truck has started every time.
Prior to, every morning it wouldn't start. Almost every day after work it wouldn't start. I would try, wait, try, and it eventually would.
I'm feeling pretty confident that they have fixed the problem. Add me to the list of guys that had the problem, got a new starter, and have been good since. The OP I believe is on that list as he hasn't come back indicated that his issue has come back.
This talk about the flapper valve is absolutely, completely not related to the non-starting issue described in this thread. The flapper is a purely mechanical device that has absolutely nothing to do with allowing the starter to turn.