I thought I needed an airspace in the hearth, like against the combustible wall, but if they say the "open faced sandwich" of plywood, cement board, mortar, and tile is sufficient, then I believe that.
Very nice! One thing puzzles me though. If backer board and tiles are sufficient protection for the framing of the raised hearth, why not just remove the floorboards in the area and replace with backer board and tiles?
Why is your dog always so ... moist? Check this tiny ad for some sort of cure: