On my system it asks between a few different public registries, and dockerhub/docker.io is one of the choices.

t's all public infrastructure for hosting container images, I don't think Docker-the-company minds other software interfacing with it. After all, they get to call them 'Docker images', 'Dockerfiles', and put their branding everywhere. At this point

By default it uses whatever is in registries.conf for unqualified-search-registries. You can specify in the fully qualified image name if you'd like.

I can't speak to what Docker Inc. is okay with or not.