If you look at stockinette stitch from the right side, you will see that it looks the same upside down as it does right side up.
Stocking stitch (stockinette) right side up:
However, you can't simply flip a stitch upside down. A stitch is not the same on the bottom as it is on the top. A fundamental thing to note about knitted stitches is they are made out of a continuous series of loops. Each loop starts from the bottom, up over the needle, and back down.
Here's a simplified diagram of a row of stitches:
Notice in this picture there are 10 stitches (i.e., 10 bumps across the top):
The bottom of the row looks (almost) like a mirror of the top of the row. But look closely, and you'll see it's a mirror of the top shifted over one half stitch. When you are grafting using Kitchener stitch, or picking up from a provisional cast on, you need to be aware of this stitch anatomy. This means, when picking up stitches to work in the opposite direction, you need to compensate for the 1 stitch shortage by picking up a stitch from the edge. You can see this in action in How to cast on: working from a provisional cast on.