It has to do with how it functions in practice, IMO. PostgreSQL itself is arguably a service, but the database probably is not - you're probably crawling all over its implementation details and data model.

You could take a stand and say, "All access is through stored procedures. They are the API." And, if that API operates as the same semantic level as a well-crafted REST API, then you could make an argument that that particular database is a microservice that just happens to have been implemented on top of PostgreSQL. But I don't think I've ever seen such a thing happen in the wild. It's much more popular to use an ORM to get things nice and tightly coupled.