VOD mutes are not the same as a DMCA take-down notice.
Twitch hired a third party company, Audible Magic, to handle automatic content recognition. Mutes come from Audible Magic. Not all music content is registered in Audible Magic — it is up to the copyrights holders to register and maintain their permissions within Audible Magic. Because of this, there are tracks that are properly licensed for use on Twitch which will still mute, and there are tracks that are not licensed for use on Twitch that will not mute. Yes, this is problematic.
DMCA take-down notices can only come from the copyrights holders. Audible Magic and Twitch cannot issue DMCA take-downs.
This is not to say that something that was muted will not receive a DMCA take-down notice. As has been noted by content creators: Twitch still stores un-muted and even deleted VODs on their servers which are searchable by content ID systems. Even if it is muted or deleted, you still could receive a DMCA take-down notice.