You're also missing another false positive, which was, as I recall, when they shut down the right engine and started their descent, they disconnected the autothrottle, which up until that point had been driving the damaged left engine much harder as it tried to match a thrust setting it could not achieve with the damage sustained. When A/THR was disconnected and the descent started, the thrust setting of the engine was considerably reduced. So in fact the vibration felt through the airframe decreased a great deal, even though they'd shut down the wrong engine.