I agree with most of what you said, but I will disagree with this one part (bolded). 1 2" thick board is much harder to break than 2 1" boards put together - for the reasons you've given. It is much harder to make a single, thicker board bow than several thinner boards put together, even if they are strapped together.
He didn't say that the two boards are considered an equally thick board, however. He just stated that they are an extra-thick board.