Misinformation strikes again.
Unfortunately, Bettas are both very hardy, adaptive fish, but can also be fragile if subjected to sudden changes, so the myth has gotten around that changing the water can kill your fish.
If you change the water correctly, you can change it every day and not bother the fish. If you just dump out the tank, refil it from the hose, and dump your fish back in, well.. that can kill him. As long as you are letting the water for the change come to the same temp as his tank (or very close) and using a water conditioner, he will appreciate water changes. ^_^
One note I will make, though -- if your gravel is the "painted" kind, sometimes that will leach stuff into the water to make it cloudy. I have had much better luck with natural gravels, and sand. I have seen others on the site use colored marbles, and glass beads when they want a more colorful tank, since those won't leach stuff into the water.