I already accepted that SE will probably not send me an invitation into the Alpha. I kind of got tired of being constantly disappointed with them or checking my e-mail at 4AM in the morning for that matter. There will probably be plenty of that when they don't invite me into Beta.

It hasn't happened to me, but I bet it is a real kick in the knee when you see that e-mail for it to just to find out it is only to apply to something you already did. Not only that, it feels incredibly insulting for the team to come into this thread and throw that generic message in there. I am not saying you should apologize reps, but if you are going to respond to a thread like this, do a better job of it.