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.
Twitch uses a tool called Audible Magic that automatically scans your VODs for copyright music and mutes it. However, the tool is not 100% accurate. Copyright music can (and often does) sneak through, leaving you vulnerable to DMCAs.
When a VOD or clip is deleted from Twitch, it can take time for the content to be fully removed from the publicly available site. Twitch has stated in an official thread on Twitter that they cannot verify if third-party tools have fully removed content from their site and that content deleted using their mass deletion tool should not be subject to DMCA strikes.
However, users have found ways to access deleted VODs and some third-party sites are archiving content from top streamers on Twitch, both content deleted by the streamer and content from banned streamers. Twitch has not officially addressed concerns about publicly discoverable archives that may contain content that was deleted from the Twitch site.