The basic argument is the same as the one used to show that short stacks are not at a disadvantage in NL. When you have a short stack, you are free to ignore the extra chips in your opponents' stacks. By symmetry, they can't get an advantage over you. However, they are not free to ignore chips beyond yours, and so they make plays which give you equity.
There are many edges in LHE. Some come from making thin value bets your opponents would not make, but there are other edges such as recognizing that some hands are profitable that your opponents don't think are playable, or avoiding unprofitable hands that your opponents think are playable. Both preflop and postflop, the correct ranges to play change slightly if you play a short stack. Your opponents will generally continue to play the regular ranges and you can profit by adapting to the effective stack depth while they do not, and can not without losing money to the other normal stacks.
I don't worry about this much in LHE cash games, but the issue comes up in the LHE tournaments I play. You can see more discussion of how to play differently with a short stack in articles on LHE tournament play, such as in the Full Tilt handbook.