It looks like Ari is trying to simplify the imagining of the 3 corner pieces together by "breaking it off" and placing it with the other corner pieces. Inevitably, as you know now, that corner piece will be behind the structure in reality when constructed. This melds well with this "breaking off a piece" strategy.
Not really, it's just a conceptual way to approach the problem. You know where the piece that got broken off is going to end up relative to another piece when it finishes getting folded, so you're able to "move" the piece in its unfolded state and you will still get the same object when folding is complete. It just groups together the pieces with shading for convenience.
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