While I think you're close to the right answer, Ktom, I think you should probably acknowledge that each of the icons represents a strength in rather different categories. The description that the OP provided does indeed correlate pretty directly to strength when considered for a military icon.
No game mechanics is going to perfectly match all book scenarios. While I perfectly agree that each icon represents a different kind of conflict, and thus a different kind of strength, why is it that a character's STR is the same for all challenges they participate in? Giving Eddard the intrigue icon makes him as effective in intrigue challenges as Varys, for example. Really?
But the earlier description of the characters with the 5 STR was meant to be an example of how such high STR for a single, unique personality that wasn't much for swinging a sword could be justified. Some of it corresponds to different challenges, sure, but it ignores the fact that the characters have other icons, and that "weaker" characters have other abilities that, practically speaking, make them more effective than these characters. As dcdennis points out:
Craster dictated terms alright. How'd that work out for him?
A good point. I mean, Dayne was, almost beyond question, the best warrior for generations. How'd that work out for him at the Tower of Joy? How'd things work out for Rhaegar? To paraphrase the man - he was brave, he was noble, and he died. Just because someone is effective doesn't mean they're unbeatable (especially in Westeros). Stealth or Deadly on an opponent's character has the potential to make all three of these guys considerably less "effective" in the long run.
What I think everyone can agree on, though, regardless of the exact model or explanation they choose, is that the STR statistic is meant to describe so much more than what is likely to happen on the tournament grounds, sword in hand.