They have. And yet, RMT and bots can't be recorded or screenshotted.
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But after the stream is stored, Twitch will still retain the information that it was from his channel, right? No third party would have been able to put that there. The important thing here is that his Twitch account and FFXIV character profile have links to each other, thus it was possible to prove beyond reasonable doubt that it was his video. If you capture a video of someone else doing bad stuff, post it to your own youtube channel and offer it as evidence, such a link does not exist.
To be fair they said WARNING, not bans
This is going in circles, it's the TYPE of third party evidence, a VERIFIED Twitch account is different than Joe pulling up something in Discord, and someone with Notepad editing the XML file, and using Photoshop on a screenshot.
Not doing in the past doesn't even matter, if it's in line with their TOS now.