What you are saying is that Fair Use cannot be utilized, because the hosting company is somehow violating copyright.
That is the same nonsensical logic that is used against MegaUpload and bittorrent; the same nonsensical logic that Youtube's Content Protection system is based on; the same nonsensical logic that drives DRM.
The world is not better when copyright holders are able to compel a third party to win their disputes. Unfortunately, that is the world we live in.
It's ridiculous that Twitch mutes audio, even if it's only a few seconds. Fair use is being totally ignored.