Have you ever played the Telephone Game? You pass a phrase on from person to person eventually winding up with the phrase being told to the person who started it. By the time the message gets back to the person it usually barely resembles the original. Such is the case with Palin's "quote" about seeing Russia from her back yard.
"They're our next-door neighbors and you can actually see Russia from land here in Alaska, from an island in Alaska"
Yup, barely resembles the original in this attempt at the game too.