All I know is that if any person at Square-Enix highlighted that the manual and the game had Aeris 100% and Aerith 0%, which I can only assume many did note (I mean, it's hard to miss, isn't it? xD), not one of these people made a decision to get that changed. Someone out there clearly made the concious decision to have all that text remain as Aeris, and that decision for me means that Aeris is the official name because it was decided. It doesn't matter who made the decision, but they clearly had the power to because that is the name she was given to the Western audience in the original game, and it has not been changed in the original game during it's re-release on Steam. There was no mishap, it was a choice and they made it and obviously had the power to make it. It's also a far more accurate translation than Aerith, unless perhaps someone genuinely had a lisp when they talked about her at some point. How is it spelt in Japanese again? Earisu or something? Definitely said with an 's' and not a 'th'.

It wasn't really up for debate until some bugger decided to start printing Aerith on all future publications, which for me was a silly mistake. They're the ones that are making typos as far as I'm concerned.