It is, but that’s part of the reason we need these agreements. For decades, too much has been done informally without formal agreements to justify it, which is fine when everything works as planned but can start to cause problems if something goes wrong.
I remember being on a Royal Navy establishment and being treated precisely as if I was an RN officer rather than an RAN officer without any clear legal principle to back that up. It never really occurred to me, or to anybody else, that might have the potential to cause problems.