Don't bother reading the opinion of an actual adcom member. Not like his opinion matters. You are obviously more well informed.
Again, like Tildy said, it depends on the person reading the application and the context it was used in. If it wasn't "XYZ is my top choice" or "XYZ is amazing because of ABC" and was simply a "At XYZ, I hope to continue activity ABC" type mistake.. I don't see it being an auto-rejection.
An auto-rejection is hard to achieve IMO. We're talking about criminal history, extremely low stats (<3.0/25), incomplete application (blank essays, absolutely NO ECs) or the like. Writing the wrong school name in an answer to a general question such as "current activities" like the OP did is far from being in this group.
You are also weighing stats too heavily. There aren't "thousands of applicants just like you" because stats aren't the only things that matter. If everyone wrote the same essays, had the same ECs.. then yea, this is a killer because some other guy didn't make the same mistake. But if the school thinks you are a great fit based on your PS, ECs, LORs and stats.. I just can't see them changing their opinion heavily based on a reference to the incorrect school made in passing.
There's really no point in arguing this because not only will we never know what will happen to the OP (unless he gets an interview) but because it is also impossible to ever find out how every single adcom member views this mistake. Tildy is evidence that adcoms do view this mistake differently.. whether that's just him/her or applies to other adcoms.. we will never know. Neither of us have opinions that are worth more than a grain of salt in this regard.