It was a coincidence that Brit and Iggy ended up with it. As far as I know The Invincible Men showed it to Britney while they were working on a different track and she immediately wanted to record it. So as you already said LM didn't have much of a choice in the end. But I'm sure they're more than happy about Britney releasing a song they wrote (by the way, I didn't know she was releasing this song first. But seems like she will if The Sun already heard about it.
Source - 1
hoping it isn't truth.