IANAL/etc, but the subsidiary and the parent are different people (legal personhood). The US parent is only responsible for the EU subsidiary’s actions under US law to the extent it has effective control of them. If the parent tells the subsidiary to obey a US legal order, and the management of the subsidiary refuses on the grounds of EU law - then the management of the parent has done what US law requires them to do. The US management might consider firing the EU management and replacing them with new managers - but if the job requirement is “must be willing to break local law”, nobody with an appropriate background is going to apply, so if they fire them they won’t be able to replace them, hence they are legally justified in not firing them.

It is normally true that a wholly-owned subsidiary just does whatever the parent’s executive management demands, but this is one of the rare cases where that generalisation breaks down. (If we consider non-wholly-owned subsidiaries, it becomes a much more common thing.)