Confirming the theory between "Stuck with me" and "Do Da Da"

Most of you already know the story, but I'm gonna copy-paste it from Geek Stink Breath for those who don't know it: Do Da Da is a part of the legend about a studio mix up that gave the name to the song Stuck with Me from Insomniac, and left Do Da Da with no title. Supposedly, the name "Stuck with Me" was given to the song by mistake - someone in the studio wrote the title on the demo, and the band then decided to keep the name since they found it fitting. Do Da Da was the original owner of that title, so the band had to think of another name for this song, and they decided to give it a meaningless title "Do Da Da".

And now, My theory. Do Da Da, is not a "meaningless title", it was actually the original name of Stuck With Me. How can I tell? There's an art movement, called Dadaism, Dada for short. The Dada art style was used to create the album cover of Insomniac as well as the music video of Stuck With Me. Out of the 3 (4) songs of Insomniac, only Stuck With Me contains Dada. So, unless it's an one in a million coincidence, Do Da Da (Do Dada?) was actually the original title of Stuck With Me, and not just a meaningless title that was given to Do Da Da cause it was left without a title.