Hung/Murray, here’s the way I look at it, for what it’s worth. On the guitar, you can change pitch in two ways: you can change the string tension by turning the pegs, or you can shorten the string by putting your finger on the fret board. The outward pull (“smile”) is more like the former, while the inward pull is more like the latter. By pulling inwards, you are actually shortening the length of lip that is free to vibrate, thus “shortening the string”.