I believe that's what I just said. Or are you interpreting it as a single damage reduction value for adamantine armor, rather than two distinct components (the adamantine's effect and the armor as DR effect), the total of which counts as a singular source from armor to stack with the Barbarian DR? I interpret each component as its own, distinct effect (as you can see in my post you quoted).
I'm interpreting it as him getting getting DR 9/- in total because they're all DR/-, and that it should therefore stack. So I guess I'm interpreting it as a single damage reduction.
Kevin's is probably the more reasonable interpretation. Otherwise, adamantine armor of nearly any type would always be overwitten by the base armor's own DR.
The way I see it: DR from armor stacks with any other form of damage reduction(due to the quoted specific rule), but the other forms of damage reduction don't stack with each other (due to the general rule)
So in this case, the DR from armor would stack with both the DR from class levels, and the DR from adamantine, but the latter two would overlap and not stack.
The final value of DR would be armor DR+the highest between adamantine DR and class level DR.