Capsaicin, the thing that makes peppers hot, is fat soluble and thus water does not counter the burning sensation. If it is cold water it will temporarily overpower the capsaicin’s effect on the nerve receptors and tell your brain you are feeling a cold sensation, but once the cold water is swallowed the heat will come back.
Dairy products work best to counteract capsaicin because they contain a protein called casein which binds to the capsaicin, hindering its ability to bind to your nerve receptors.
Drinking milk before or while eating the peppers will help reduce irritation in your intestines for the same reason it helps in your mouth. It could save you from that awful day after burn.