Surely you can see that we could apply that principle to either pro- or anti-euthanasia arguments?

Either way, the government is profoundly involved.

Either the government is in the business of telling us we cannot end our own lives in humane and medically-assisted ways, and that medically assisted deaths are equivalent to murder with all of the attendant legal issues.

Or they are in the business of enforcing rules about how those medically-assisted deaths can happen.

It’s the government’s choice whether they allocate resources to investigate and prosecute “suspicious” deaths of terminal patients.

Deciding as a matter of policy, not law, “No, we don’t do that outside of extraordinary circumstances” is something a government institution can do.