Toyota a full of it, sorry.
I've seen two brand new cambelts chewed up by (silent) old tensioner and idler. Changing the belt and not changing them is foolish! Unbelievable that they say that. Lexus Bristol wouldn't change my belt without doing the tensioner and idler!!
The reason to get your water pump done at the same time is because if it does go, and it will, you said yourself it's the original on the car, then you save labour charge as they have to remove everything around there when doing the cambelt anyway so it'll just cost you the cost of the water pump (about £120)
To replace water pump including labour is about £300 so you stand to save £170 in the long run.