Yup, that's correct. In fact, all NPCs have unlimited arrows.
Oblivion had the same system, and there was a guy training in the arena bloodworks, hence the previous comments.
You missed the oblivion forum...by 5 years.
Those were iron.
I know, the difference in damage and value is astonishing. :B
On a more serious note: not everyone playing Skyrim has played Oblivion before.