Unfortunately, I don't think we can say that they should.

I mean, in democratic ideology they should, but democratic state institutions, legal and organizational arrangements are not fashioned to achieve this outcome; and most democratic states were not, after all, created by the mass of people setting up those arrangements. Rather, elite groups and powerful interests set such states up, with democratic elections being a mechanism for legitimizing the new regime among the masses, or a concession to public pressure.

If a big American corporation is transferring lots of money from Europe to America while engaging in some sketchy behaviour, Europe might be more enthusiastic about clamping down on that than America. For both financial reasons and due to different political priorities.

It's not like Europe could unilaterally reverse Google's purchase of Youtube or Facebook's purchase of WhatsApp.