It depends what's causing the eyes to tear, and for some reason distilled water helps some puppies who are teething. Distilled water is different than filtered water, distilled water take all the minerals out of the water. Bottle water is just "purified" and certain chemicals are reduced, but minerals are still there. Here's a good link, and it tells of the different things that cause tearing.
Tear Staining: The Causes & Cures