They anticorrelate in some locations. In others, they don't. Here in Finland in the winter you get effectively zero sun. We also get persistent stationary anticyclones. That means potentially over a month of temps in the -30°C region, and zero wind.
Australia is extremely sunny. California is even better, they are modeling that assuming they keep their current hydro capacity, they only need to add ~3h in batteries. Hot places also do better than cold places, because the usage peaks track the sun.
> In Europe or America you might need 7-8 while in carbon industry PR models (the same people who denied global warming) seem to think you need 300+.
How on earth do you expect 7-8 to be enough? 300 isn't enough either. The real number for a fully renewable-based grid here is somewhere north of 2000.
Renewables are great in some situations. There are places in the world that should go for 100% renewables as quickly as possible. It also makes sense to locate a lot of the high-consuming industry in such places. But before you hawk your solution everywhere, you need to actually study the local conditions, and not try to extrapolate anything from Australia.