I agree Brian, but this would be a rather unusual case where severe amounts of perspiration was lost (Salts + water) and only compensated by drinking water (lacking salts). If you are eating regularly and not losing massive amounts of water to perspiration I doubt you would run into this kind of problem. The small amount of minerals found in mineral or spring water don't really contribute to the osmotic pressure of your blood. Sodium is the main factor regulating total blood osmolarity. Drinking iso-osmotic fluid would be the best, it actually tastes salty - like the blood from your bleeding lip. A lot of sports jocks/meds recommend gateraide diluted by half as a near optimum formulation of water + salts + sugars.
[Edit] - one area where distillation could be useful is when encountering brackish or salt water. Distillation could be used to make this water drinkable, albeit at a cost of fuel and time.