And looking a little further down, how did a Heavyside Step function get invoked?A little of both. When you start a physics proof with "assume [such and such] reference frame" with no actual reasoning behind it, I feel you're already cheating. You don't invoke relativity just because classical physics gives you weird answers. You invoke relativity when there is a disconnect between two IFR. For flipping someone across balconies, the observer has a pretty reasonable frame of reference.
But I'm with you @Hexokinase. I'm calling shenanigans.