Imagine the same kind of position in the physical world. A multinational storage company would be forced by the USG to open up a client's storage locker somewhere in Europe, copy all the documents in it and send them to the US.
If nothing else this is a very serious threat to the US as the global provider of tech services.
MI5/6 doesn't go 'oh poppycock, they've hopped on the chunnel and fled to France.' They talk to the French agencies or if it's too secret, they go and do it them self. Mossad doesn't give a damn where in the world you are.
'Everyone, everywhere, our laws only exist in our country' is, and has been for a long time, standard operating procedure for these agencies in every country for basically their entire existence.
I didn't change the topic at all. I can't quote the relevant laws in this case but as far as I know the law in Europe is that you need a warrant to get the information and that requirement doesn't disappear if the owner of the information is a foreigner.
That's what's truly amazing in the USG's position. I agree that everyone tries to spy on information on the wire, but the idea that you can demand any information at rest from any company as long as the owner of the information is a foreigner is an amazing position to hold.
There are two other reasons to move your data to your own jurisdiction from US services. 1) the US has the most well funded military so your local spooks probably have less capabilities 2) if one of your local spooks spies on you at least you're in the same jurisdiction and have a small amount of agency (the courts, the vote).