It doesn't really matter when it doesn't work. It's essentially false advertising. Watch some reviews and see for yourself.
Ah, the 'watch some reviews' proof! Curiously, watch some others and you seem to get a different answer.
By the way, we will get some idea of how 'false' the advertising is because there are some parts of the world where you can't just put any old crap in your ad, since the law says it has to actually be truthful. It's interesting to me how few of the claims of Apple's 'false advertising' are actually challenged, let alone upheld, in those places.
However, the OP's question was whether the coating (whether effective or not) is only on the top of the MBA, and the answer is that as far as I can tell from the 15-inch midnight MBA I'm using right now, and have been for most of the day, and the lack of smudges and marking on the wrist rest either side of the trackpad - no, it's not just on the top panel. Even the trackpad isn't smudging much. I also wipes clean pretty easily.