One thing is that usually the local server would be owned and managed by a local subsidiary of that foreign company - it may even be a requirement, to have them be run by a local company (even if fully owned by a foreign entity) with local responsible officers.

Another issue is establishing jurisdiction; if the server is held locally, then it's clear that local laws apply to things done on that server - the owner of the server can't claim that they e.g. got a US subpoena and did some stuff in USA that fulfills all the USA legal requirements and everything that's it; if the server was physically located in e.g. Canadian soil, then it means that the violation (if any) happened "in Canada" even if it was done by USA-located USA citizens of USA company.