Not to be rude, but think about where turtles live and then tell me that the dirty water isn't good for them. Our turtles came from canals and ditches and ponds that are often more stagnant than the tank water they are in.
The turtles have a good filter to keep the water as fresh as possible without changing the water completely and it gets change every so often with a deep clean to get all the shells and built up gunk out of the gravel. Our turtles are happy and healthy.
I'm not saying to never change the water, but I know of people who change the water and clean out the gravel once a week and this will definitely stress out the turtles and weaken their immune system. This is what I was referring to.
I live in Louisiana and many people just go out and catch turtles in ditches and expect them to adjust to having their water changed several times a week in the effort to keep their tanks clean. These turtles are used to muddy water at the very least. With some other turtle breeds, this might be different, but in this case, changing the water out too often will be detrimental to their health.
Changing a portion of the water would be a good idea but we haven't had to do that with ours because we have a good filter that keeps their giant tank fairly clean for quite a while.
There are natural chemical cycles in nature that aren't going to be present in an artificial environment (your tank). I think you're misunderstanding me. When I say that the water is unsafe, I don't mean because it's "dirty" or "muddy". I mean because of the water parameters--the stuff you can't tell just by looking at it. Ammonia, nitrites, nitrates, pH, hardness, etc. Ammonia, for example, is extremely dangerous to animals but it's invisible to the naked eye. You could have a tank that seemed sparkly clean and there could still be ammonia present (this is when test kits come in handy). I have a mud turtle, I don't mind mud in my tanks!
In nature, you have a complete ecosystem with plants, rain, and tons of organisms (many that we can't see) to keep things in balance. An aquarium is not balanced like that. You'll end up with some beneficial bacteria to help break down ammonia and nitrites (you'll lose them if you do 100% water changes which is probably where you got the idea that water changes cause health problems) but it's not going to be anything like in the wild. Most aquariums that are cycled still don't have full cycles, either. The ammonia gets converted to nitrite and the nitrite gets converted to nitrate. But the nitrate usually just sits there for the most part, building up. In small amounts it won't hurt a turtle but in the long run it's going to cause stress (and eventually illness). Meanwhile, the water is usually going to get more and more acidic. That's why aquarium owners perform partial water changes. Doing a small water change will keep nitrate levels low and help the pH stay stable.
Oh, and filters might make the water look clear. But that doesn't mean the tank is stable.
I really don't want to debate this, honestly. If your water change routine is working for you and water tests show your aquarium to be safe, good for you. Don't change what you're doing. But please don't tell people not to do water changes--most people aren't going to be as lucky! You'll also confuse people who have smaller tanks that NEED water changes or turtle species that are sensitive to water impurities.