No bowler has ever taken decent hauls of wickets consistently just by bowling with good accuracy. Yes, Broad does sometimes have the ability to do that (also still sprays it plenty regularly enough), in fact always has done, as long as I can remember him. But it isn't a wicket-taking tool in itself - it's a run-restricting tool and one that enhances, greatly, the potency of any wicket-taking weapons a bowler possesses (as high pace does) but isn't a wicket-taking tool in itself.
If Broad gets his lines right, bowls a full length, and the ball swings, he's deadly, like we saw at The Oval. But there are several reasons why we've only seen that on tiny numbers of occasions - one he routinely bowls too short, two the ball doesn't swing that much outside England at the current time (only recently that it's started swinging properly again in England anyway), three he's still prone to spraying it.
In the Caribbean in 2009, for instance, Broad bowled generally decent areas on mostly flat decks and emerged with some amount of credit, given his extremely poor previous performances. But even against some pretty moderate batting, he hardly dominated. On more flat decks against really good batting like the Australians', I don't see him emerging with remotely good figures even if he bowls as he did in West Indies.