Darkstar, are you saying it's OK for turtles to live in water with high ammonia/nitrite levels, or are you simply saying that you personally are able to keep up with the water changes enough to keep the concentrations of these chemicals down enough?
Because a high ammonia concentration in the water (as suggested by the presence of nitrite in the OP's test results) IS bad for turtles, obviously ammonia at very high concentrations can irritate the eyes and other sensitive areas, but the main issue is the fact that water with high ammonia/nitrite levels is going to harbour a whole load more of potentially dangerous bacteria, due to the fact that these nitrogenous compounds are resultant of faecal matter and urine in the water not being broken down properly.
When there is no detectable ammonia in the water, this is because the urine and faecal matter
are being broken down properly by bacteria in the filter, so the bacteria have nothing to live in/feed on.
I've seen in many cases how bad water conditions lead to shell rot, and especially with more sensitive species of turtles like soft-shells, infections resulting from poor water conditions are far more common and more often fatal.
It's true that turtles are nowhere near as sensitive to nitrogenous waste as fish are, but to say "biological filtration is pointless" is just wrong, and that a turtle tank "doesn't need cycling" is just a more risky way of going about things. Sliders are pretty hardy turtles, but I wouldn't recommend going without a filter and exposing them with bad water conditions just because they can often just cope with it.
And if your saying that you can do enough water changes to keep the ammonia concentration down I can only presume you have a young turtle, otherwise...well, that's no small claim - as we all know how messy these guys are

. Although from your wording you could just even be saying that you merely top up for evaporation

.