Ok, I'm gonna wade in here. I'd tuned my previous car, a Focus ST. Plenty of very good tuning companies around for this model, however, I used Mountune even though my car was out of warranty. Why? Because if anything major went pop, I know Ford wouldn't just blame the tuning as it's covered by them - regardless, I'd have to pay out, but it added peace of mind.
Would I modify the S3? Not until some company comes up with an agreement with Audi that the warranty is covered in the same vain as Mountune & Ford. Don't get me wrong, swapping out the exhaust for a cat-back or de-res is okay in my mind, as it's hardly adding anything other than noise imo - but full on maps etc are a big 'no no' if you want to keep your warranty intact.
I agree, why should Audi cover the cost of parts that have failed because you've added extra stress to those parts by modifying the car. That's not fair on Audi and by trying to cover it up, you leave yourself open to all sorts. Why bother. Once it's out of warranty, do what you want, it's your car... your risk.
A lot of people just bolt on a re-map and get all the extra power etc they're after. But I'd want to back this up with other modifications to the cooling and braking systems. Not to mention the extra stress on suspension and drive-train components. If you're adding in another 100bhp, you'll need to make sure everything is upto the job to avoid failures.
So in summary... if you want to modify it in warranty, say good bye to the warranty from Audi. It's your risk. Audi are fair, if you added a new cat back and your damper failed, then this is pretty unrelated imo and they'd probably be okay with it.