Well -- I have read the information on these sites. No where does it say it is better for the turtle than a naturally cycled tank. In fact -- it does they don't even address it.
Turtles do breath off the surface but also absorb oxygen from the water through capilliaries in their nostrils and cloaca.
So swimming around in their own ammonia waste for any length on time is not the best thing in the world for them. If you proper cycle your tank, then introduce your turtles into it. Ammonia will be combatted thus making a healthy natural situation for animal.
Yes, weekly changes are necessary to remove nitrates from the water and of course you should use a gravel siphon to get the broken down material out of your gravel but that is all that need be done in a balanced tank.
If you keep a turtle pond do you do 100% weekly or monthly water changes with that? Of course not. The water maintains itself naturally and the turtles thrive.
Breaking your tank down once a month certainly won't hurt MOST species of turtles (there are several species that MUST have a properly cycled tank) but it is unnecessary and your turtle will do quite well in properly cycled tank.