Why not? It's exactly the same question that I originally asked - but different classes.
What's the difference?
I would love to be proved wrong for a number of reasons, in Europe Turbine aircraft require a type rating regardless of weight and this does not carry over under automatic privileges as I understand it.
I have a number of type ratings on my JAA licence that would not require type ratings on my FAA licence as they are under 12,500lbs.
It is possible to get approval from certain states providing satisfactory training can be proven. But it is a state by state basis and on named types, not a blanket covering.