Here's why not to let your chameleon have access to stagnant water. Even if the water is in motion via recirculation, over time bacteria will build up in the container and inside the water lines. It really doesn't take a lot of organic matter in the form of a piece of shed skin, plant matter, insect body, etc to create a nice bacterial broth.
Now along comes your chameleon who drinks this bacteria laden water. Then your chameleon channels some of this water through his sinus passages and into his eye turrets for cleaning and WHAM! you get a nice little infection.
Now add to this a little stress like being a bit under hydrated, or stressed from captivity and its a recipe for disaster. Chameleons are extremely dependent on vision. And even if one of there eyes isn't working properly they can't aim properly and will begin to malnourish.
Once your chameleon gets sick it's a real fight to get him/her back to good health.
Chameleons can be dead difficult to properly care for in the first place. Don't shoot yourself in the foot for the sake of simplicity.