Ehh. Birthday is an amazing song but it doesn't feel like lead single material to me. Surely she was talking about Legendary Lovers, or maybe Walking on Air? Roar's was a much better choice than Birthday if that was the choices.
Walking on Air and Birthday are also the two potential 2nd and 3rd singles prior to the actual choices. Poor songs, always being pushed back.
I doubt "Walking on Air" was ever a contender for the lead. It would've been far too risky of a choice to start the era off, at least stateside.