It is not the alt that you climb to per se, it is the rate of change that you are subjected to. We have microbubbles in our body at the end of a dive even after having surfaced normally from either a correctly decompressed dive of from a no stop dive. These bubbles are expelled from our body over a period of time following the dive down to a back ground level. There is always a "background" of bubbles present, a doppler easily verifies this.
A rapid rate of change in pressure can cause the microbubbles to seed, essentially they all decide to wander off to a rave and make new friends. Little bubbles that did not cause problems suddenly grow in size and room has to be made for them. This happens in the form of tearing of tissue and nerve, blockage of veins and arteries etc which then presents as clinical DCI.
There is no such thing as an immunity to a bend, it comes down to carefull decompression and luck. The incidence of bends against time in water is pretty low if the basic rules are followed.
As BB points out his physics are correct on pressure changes. There are some complex issues around the subject as well along with some interesting spanners that can appear in the works PFO being one of them. They arguments continue to rage as to how many and what type of tissue compartments represent the human body. Haldanian, Buhlmaan, DSAT, Comex etc. At the end of the day they are just mathematical models.
AS I said before, the agencies recomendations are good, reduced liability etc. We make our own choice based on knowledge and experiance.