I don't think this is entirely true, insofar as non-local models inherently have a "man cannot serve two masters" problem. The end user and the org running the AI may have different goals. That means even if AI alignment were to be in some sense "solved" for local models, you wouldn't be guaranteed an aligned AI using a non-local model because the "owners" of the non-local model may have deliberately misaligned the AI in their favor and against your interests.

How so? If it's not local, it's not yours, a third party owns it.

Why would you expect that third party specifically trained their model to be more aligned to you and your needs than to them and their (business) needs?