Giving them bottled water may or may not help, but it certaintly would not hurt to give it to them. It all depends on what the tearing is from. But yes if the tear staining is from the water, switching from tap water to bottled water will improve the tear stains and I have seen many dogs where this is all you have to do and it clears up the tear staining. There are many things that contribute to tear staining such as:
Genetics
Cutting teeth
Poor diet
Water
Over active tear ducts
Eyelids are not deep enough to catch or collect tears resulting in constant tearing
I give mine distilled water ( I heard it is the best type of water to give them, be careful some bottled water has sodium in it which is not good to give), Chicken Soup dog food (which is suppose to be great for dogs that have tear staining), and my maltese is now getting Angel Eyes which is working great!!