This is the thing which is not the case. The subsidiary in the US is nearly always a different company than the one(s) in Europe. They'll have different management and different lawyers etc. Sometimes they even have different owners, e.g. because one of them is a joint venture with some other company, or a franchise. And they have to be different, because different countries have different laws and those laws often conflict with each other. So the subsidiary in the US follows US law and the one in France follows the law in France.

You could try to make it otherwise, but it's pretty obvious what would happen then. Companies couldn't formally operate in multiple countries because their laws are incompatible, so instead there would be a straw front company in any given country that nominally isn't owned by the conglomerate, but is effectively just reselling their product/service in that country for an additional margin that only pays the salary of local management. To prevent this you would have to ban companies from having foreign suppliers, which is not very practical.

And since countries know that's what would happen, they allow foreign subsidiaries to be regarded as separate entities even if they have shared ownership, instead of demanding the charade.