Even putting aside all the good arguments made so far against dragons having total immunities, there is one very good reason that dragons should not be totally immune to the element of their breath weapon: it is inconsistent with myth and fantasy.
I have seen many cases in fiction and myth in which the only possible way to kill a creature is to use its own weapon against it. Things like "the Nemean Lion's hide is invincible to any blade, but its own claw can cut it" or "the only way to kill the beast is to reflect its own power against it". Things may be resistant to their own powers, but they are almost never totally immune to them. In fact, I have seen a few cases of a hero killing a dragon simply by reducing the dragon's own resistance to its horribly overpowered breath weapon.
Also, on the amusing "humans are immune to water" thing...
Jellyfish are made of something like 90-99% water. They are aquatic creatures who breathe water, and could not survive outside of water very long.
I guarantee you, if you put a saltwater jellyfish in fresh water, fresh water would pour into every cell in its body at a very fast rate, and every cell in its body would rupture, killing the creature very quickly. It would die from nothing more than contact with water, its native element.
Also, human breath air through our lungs, but if a single bubble of air forms in our bloodstream it can very easily be fatal.
A lot of living things can be killed by things they interact with on a constant basis, simply by getting past the physical barriers they put up to protect the fragility of their own internal systems.