Maelstrom, here's a more elaborate explanation.

The crank length determines the pedal circumference. Using a shorter crank makes a smaller circle. However, using the same length cranks with a spacer (or a pedal drop extension) will have the same circle circumference. The spacer (or drop) is only changing the foot's OFFSET to the pedal.

Or think of it this way. Let's look at the side of the bike with the shorter leg.
Imagine taping a marker on the bottom of your shoe, marker facing to the side, away from the bike. Then imagine putting a sheet of white cardboard parralel to the bike, so the marker can draw a circle on it.

So using a shorter crank, draw a circle . Lets call this Circle A. (the bottom bracket will be the center of circle A)
Now put on a longer crank, the same size as the other side, and add a spacer between the marker and the pedal. ( with the spacer width the same as the crank length difference ). Now draw a new circle, let's call it Circle B.

This circle B will be larger and it will touch circle A at the bottom (near the ground). However, on the upstroke, circle B will come higher than Circle A. Or in other words both knees come to the same height on the upstroke.
If you used a shorter crank, the leg extension would be the same, but the knee would not come up as high as the other side.

Get it?

This is healthier for your body, because the muscles stay in symmetry and keep the same range of motion.

By the way, Benoit,
I reread your post more carefully and honestly i'm not sure what you should do, you have a case i've never heard of, and like eric said i'd get doctors advice.