Also, you asked why you would die for the opposite of taking in too much salt. So for distilled water (lets say drinking an insane amount in 5 minutes), the blood cells would swell and burst (like you said) and the surrounding vasculature would be hypotonic. This would lead to vascular collapse....MIs, brain death...and so on due to no effective volume.....almost like if someone is in cardiogenic shock.

I would also add that electrolyte balance in itself could lead to death due to cardiac arrhythmias. Cardiac muscle does not contract properly when potassium, Ca2+ and so on are disrupted. I think the osmosis effect would probably kill you first though. As a medical student, I have seen the effects of potassium imbalance, the most likely to cause V-fib (at least with hyperkalemia).