Distilled water can and does indeed contain dissolved oxygen. Immediately after distillation it will have little to no dissolved oxygen because water at the boiling point will contain no dissolved oxygen. However, if left exposed to air, the water will pick up oxygen from the air until it becomes saturated.

I would imagine that if the distilled water were bottled shortly after distilling and the bottles were sealed, then the water within those bottles would have very low dissolved oxygen because there is very little air within the bottles. If you wanted to put oxygen back in, you could do so by bubbling air through the water or simply by leaving it exposed to air. Also, the colder the water is, the more dissolved oxygen it holds (until it freezes!).

But I still don't think it's a good idea to drink it!

Mich