Yes, you are mostly right. But there is no shame in outsourcing some of the work to Tesla as they are part of the Daimler/Aabar family and are pretty advanced in lithium battery technology and also hold many important patents.
As for carbon fibre technology. It's a long game. I'm not worried about the perception of Mercedes lagging BMW because BMW has a small volume niche production car out first. No one has got it all figured out on how to produce a volume-production model platform out of carbon. Everyone is only talking hybrid construction in using carbon to replace certain steel chassis components such as body panels, structural parts that are out of sight. NOT a wholesale move to carbon.
I will give a medal to the first car manufacturer that commits to building a full scale production line dedicated to carbon fibre. I was told the pace of adapting aerospace carbon to automotive applications is slow and the weak global economy is not helping. Also, there are still other low hanging fruits that car manufacturers are picking to reduce fuel consumption and emissions before they have to take the expensive plunge and move to carbon en masse. For the foreseeable future, carbon will remain the preserve of high-end sports and luxury models (the i3 being the exception, perhaps).