That doesn't make any sense: there is a big difference between when a chemical dissolved in another, and a chemical binding to another.
Blood, for example, is a complex solutions containing various vitamins, minerals, hormones and cells.
The water you drink is absorbed into the rest of your body and is added to the different fluids bodily (blood, lymph, cytoplasm, etc.).
Then, as your kidneys filter the blood, they pull out wastes like uric acid, and the water they are dissolved in.
So you drink water, this new water is added to other water that already contains minerals in it, resulting in more water with stuff dissolved in it. At this point the new water and old water are indistinguishable, and act the same way.
Nothing is expelled from the body's fluids until the kidneys do their job of filtering the blood.
Also, water isn't absorbed until it gets to your colon. So if you drink water with your food or within a few hours of eating, some of the minerals in the food that is in the process of being digested (from your mouth to your stomach to your small intestine) will get dissolved in the water as it makes its way to your colon aka large intestine.
The only way distilled water could be bad for you is if you are replacing water containing minerals that, unless you drank them in your water, you would be deficient in, which is the case for almost nobody.