That is describing the lawyers goal, but technically the summary judgment order by the judge didn't find that the song was in the public domain. The order did find that the defendants had zero proof that they were assigned the rights to the song.

Basically the judge found that Warner didn't own the song. But didn't go so far as saying nobody owned it.

The order says: " Because Summy Co. never acquired the rights to the Happy Birthday lyrics, Defendants, as Summy Co.’s purported successors-in-interest, do not own a valid copyright in the Happy Birthday lyrics."

There are real questions to whether the song is actually in the public domain. The date of authorship is unclear and some the actions undertaken by the alleged authors might have sent the work into the public domain.