It would not explain why it was registered under the Fifth Harmony name. What would explain that is if the song was created in 2015, and when they enlisted EKB for 7/27, he passed the song to them. Being a writer for an era is different than pitching demos. They actually recorded Big Bald Wolf, so it would make sense they were handed OOTD in 2015. BBW was also registered before being released. Nova's version was not successful, and it wasn't even released. The song has no mention before 2015, even on Nova's part, so I'm pretty sure it was her song first. Nova doesn't write for other people, either, usually.
Even in the case of sound, Harmonizers insisted for years that All Again was a Reflection outtake because of Meghan being a co-writer; despite it being well known, she did work for both eras. All Again 100% sounded 7/27 as opposed to the soundscape of Reflection. They said that Ladder was Reflection despite Leaks5h saying it was 7/27 while ignoring that Double Vision shares credits with 3/5 of the composers for Voicemail. Yet, leaks5h specified that Double Vision was a Reflection outtake, and somehow people went with that, but not Ladder. No era is defined by sound, especially not 7/27.