You’d probably have gotten more colorful answers had you posted outside of GQ, but since we’re here:
Put yourself in Palin’s position. This means that everything she says gets maximum benefit of the doubt. Read about a scandal? Read it with facts and assumptions most favorable to her, and consider everything she’s said to be either completely honest or fully believed to be honest. Also, consider the number of stories that went nowhere — Trigger as her grandson, for example.
Regardless of who made up those stories—and however they came about they were necessarily invented—it was the media that carried them, and the media that gave them credence. Furthermore, irrespective of what others think the reality was, to her it was the media who painted her as X, Y, and Z — maybe she made a misstep or two, but there was a lot of gotcha journalism involved.
If it helps the imagination, consider things from the opposite political spectrum’s point of view. Or take it back to a full belief that the Swift-Boating of Kerry was wholly unfounded and unjust (you don’t have to believe this per se, but it’s just a thought experiment). Stories were planted and reported on that hurt her/his credibility and polling numbers. Even the whisper of it will last longer than the basis.
Can you imagine yourself — if not, just read some of the Fox news Pit threads — yelling at the media to knock off all this partisan shenanigans? Palin aside, wouldn’t it be better if the media was less sensationalized and cared less about the gaffe of the week? Do you think that after the last campaign, Cronkite was unabashedly proud of the job the media did? Again, whether or not you personally agree, I’m approaching this in a GQ-like answering for her frame of mind.
If one does extend this degree of benefit of the doubt, she makes sense (no comment, in keeping with GQ).
As for the troops bit, I think that given her background and familial relationship with the military, it is a natural interjection. It’s a “For the love of all that’s holy!” or “Won’t someone think of the children!” type phrase, meant to invoke some solemnity in what follows or secure a modicum of discrete attention to what comes next.
Alternately, you can cast all the above in a bucket and go with a more mercenary view: she is about to embark on an ostensible political king-maker career (i.e., campaigning) and a lucrative book writing and talk-showing stint. Funding for all this is going to come from a solid base, a base that reacts strongly to mentions of troops. Furthermore, she has learned from the past decade or so of media marketing (see Fox, Rush, etc.) that positioning yourself as an alternate, truthful source of news against the monolithic and nebulous “mainstream” media is a successful niche. “Us against Them” works wonders for keeping an audience.