American corporations don't want to accede to european rules about access to data, but it would be grossly simplistic to say all the problem lies on either side. I am not an EU resident but I tend to think there are sound reasons for some of what they want, and as American corporate entities the majors are bound in some tricky issues around US state department expectations, FTC expectations, but it isn't just trade, it's also civil liberties and privacy-vs-security political autonomy issues.
I would have preferred the companies like this emerged as federated entities and european data stayed in european DC and was subject to european laws. I think it would have avoided a lot of this, if they had not constructed themselves to be a single US corporate sheild, with transfer pricing on the side to maximise profit.