The "Rear Sync" setting available in some cameras simply causes the flash to fire at the end of the exposure, rather than the beginning. I thought its only purpose is to cause the blur to occur in the appropriate direction.
For example, from here:
Both images show the same object moving in the same direction
However, in his book The Digital Photography Book, Part 2, Scott Kelby makes the following claim:
Changing to Rear Sync makes the flash fire at the end of the exposure (rather than the beginning), which lets the camera expose for the natural background light in the room first, and then at the very last second, it fires the flash to freeze your subject.
Why would the flash firing at the end, rather than the beginning, cause the background to expose more? Would the background have the same amount of total exposure regardless of when the flash is fired?