Actually, I’m well aware of the original song’s intentions. That doesn’t change the fact that the message is entirely changed in the new version. (In this case from sarcastic satire to direct honesty.)
As for your failure to understand my Rainbow House example, perhaps the problem lies in your trying to view the rainbow flag as the modified and owned object, and not The White House itself, as well as with your inability to realize that the White House is more than just a structure - it is a symbol. Painting it rainbow colored would have exactly the same sort of impact as changing the lyrics to a song.
People have been changing song lyrics - and in the process the meaning and significance of the song - for all of history. “God Save The Queen” of Imperial Britain became “My Country, Tis of Thee” of Imperial America. The pro-war “When Johnny Comes Marching Home” became the decidely anti-war “Johnny I Hardly Knew Ye”. The tune, the melody, the cadence, and all the bits and pieces of the music itself may be identical, but to say that the song is unchanged, that the meaning isn’t turned entirely on it’s head, is absurd.