The “faulty foundation” is that of those who say Palin resigned to run for President and say “what a stupid move for anyone wanting to run for President!” What has she said or done to indicate that she resigned to run for President? NOTHING. They are throwing darts in the dark and claiming to have hit the bullseye. In reality, they don’t have a friggin’ clue.
They're speculating that Palin is indeed running, precisely because she didn't foreclose that possibility in her press conference, or in any subsequent statement. In fact, when things are said along the lines of "higher calling", fighting for America in a different way and the like, it's fuels the speculation. And Palin knows it.
She could have easily addressed this, as Hindraker points out. But she elected not to. My common sense tells me that wasn't by accident. Others seem to agree.