Ding Ding Ding! we have a winner! To be a boxer, each pair of cylinders must move in opposition to each other. So both are at top dead center at the same time and at bottom dead center at the same time. To do this, the opposed cylinders must have separate crankpins. If they share a crankpin, one side is up while the other is down, so the unbalance cancellation achieved by a true boxer is lost.
The Ferrari 512BB was technically a 180 deg V-12.
Your explanation was longer, but much better, than mine.