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Unfortunately, AT&T can pretty much do what they want. I suppose the obvious answer is to use a VPN, but that is no iron clad guarantee. It isn’t like a court of law, AT&T (and other ISPs) don’t have to prove anything, and you’ve probably given away your right to go to court anyway under the terms of your contract with them.
Not infringing on someone's copyright certainly should be Tip No. 1. It would be a shame if you stop doing perfectly legitimate things because you're worried about getting a warning letter. The first four warning letters under the Copyright Alert System are just that, warnings. Steps 5 and 6 vary depending on the carrier, but even in those cases AT&T (at least according to this article) says it won't throttle those customers' speeds. Rather, it will force them to watch educational videos on copyrighted content online.