The short answer is that Dr. Luke technically had the ability to block the release, but declined and allowed the song to come out. Zedd confirmed as much with a tweet on April 27: "Just to clarify: We didn't use any loop holes. Kemosabe / RCA gave us permission to release this song!" Luke replied "Thanks for the clarification @Zedd ..."
This new track is particularly significant following New York Supreme Court Justice Shirley Kornreich's decision in February to deny Kesha's request for a preliminary injunction that would have allowed her to record new music without the involvement of Dr. Luke and his Kemosabe Records label. At the time, one of the key reasons why Justice Kornreich denied the request was Sony's and Luke's insistence that they would allow the singer to work on music without Luke's involvement. (Kesha's team has since appealed the decision.)
In the days following the judgment, Zedd reached out to Kesha on Twitter and offered to produce a song for her, which led to recording sessions, a surprise appearance by Kesha during Zedd's Coachella set last weekend and, now, a new track. But while Luke may not have personally been involved, Kemosabe Records still is: the track was released by Interscope (Zedd's label), RCA (the Sony Music subsidiary to which Kesha is signed) -- and Kemosabe, which still has Kesha under contract.
This, then, was the situation that Sony and Luke were promising in fighting Kesha's earlier injunction, but is not the battle that Kesha was fighting, as Luke is still benefiting from her recorded output through Kemosabe. But it also doesn't signal that a settlement is on the way. On April 3, Kesha took to Instagram to say she was offered a settlement in exchange for a public apology, which she summarily rejected, writing, "I will not take back the TRUTH. I would rather let the truth ruin my career than lie for a monster ever again."
Two days ago (April 27), Kesha's mother Pebe Sebert dropped counterclaims filed against Dr. Luke in Tennessee that alleged intentional and negligent infliction of emotional distress, following a Luke filing for defamation and tortious interference. But sources on both sides of the situation tell Billboard that there is still no settlement, despite these recent developments seeming to ease some of the tensions surrounding the situation.
Still, releasing "True Colors" could represent a path forward in Kesha's battle to separate herself from Kemosabe -- though the larger legal battle over Kesha's allegations that Dr. Luke raped and psychologically abused the singer is still far from being resolved. (Dr. Luke has denied all claims against him.) The song shot to No. 3 on Billboard's Trending 140 chart within its first 11 hours of release, and if the song becomes a hit it could re-demonstrate Kesha's viability as a commercial artist. Whether that would be enough for a new backer to offer to buy the singer out of her Kemosabe deal remains to be seen. But for now, for the first time in more than two years, Kesha is back to releasing music.