Keeping hydrated safely in Mexico

We use a pitcher of water, which is bottled, to brush our teeth while in Mexico City.

We got into Mexico City last night. Our friends Iris and David picked us up from the airport.
We navigated our way to their neighborhood–Condesa, which according to David is the Rockridge of Mexico City. (If you don’t know Rockridge that means you probably haven’t visited us in Oakland.)
When we got to their house one of the first things I asked David was about the water. They have a big jug of bottled water in their house. They use it to make coffee, to drink, to brush their teeth, to take pills, etc.
It is an interesting experience brushing my teeth over the sink with a pitcher of water in hand.
I am used to being able just fill up my water bottle wherever I go. I have always done that in Europe. Though “free” water is harder to come by in Europe. If you get water at a restaurant you usually have to pay for it.
According to FAQs on All About Mexico City, in most hotels and restaurants, you will get purified water, if in doubt – ASK.  (Agua purificada, por favor.)  I would not drink the water from a private home or condo, unless you know there is a purification system installed, and working.  Buy bottled water; why not be completely safe?  Don’t take the chance of ruining your vacation?
Some message boards people claim they drink the water in Mexico and have no problems at all. I figure it is better to be safe than sorry and just drink “bottled” water. Especially since it was advised to us by our friends.