They probably should. I've seen people concerned a subsidiary's GDPR fine would be calculated on the basis of the parent company's global revenue, and in Musk's case something similar has happened in Brazil where Starlink's assets were frozen and justified in part because of how Musk fails to properly delineate between his businesses.

The EU also lacks incentivizes to not harm SpaceX. The US government as a whole, and DoD in particular wants SpaceX around to deliver cheap mass to orbit.

Europe on the other hand would love any judgements which give their rockets a chance to catchup. So they won’t temper an investigation or fines accordingly.