There can be overlap. Do predoctoral internship applications still count assessment and intervention hours accrued in master's training? If not, they used to. The problem isn't that the training is impossible at the master's level, but rather that there is no consistent standard for master's training. By contrast, all APA-accredited programs provide coursework and supervised experience in psychological assessment. A program cannot be accredited without these features, since assessment is a core competency. We can debate what constitutes "adequate," and some contend that APA's requirements are too lax/minimal, but we know that accredited doctoral programs provide a certain minimum standard of training in assessment.
What you described, i.e.,
...sounds unusual and is probably not the norm. But what do I know? It's difficult to know because master's programs in psychology are not held to any set of consistent standards of clinical training. Even if they were, it doesn't stop a given program from going above and beyond the minimum requirements. That doesn't equate to a higher level of training for licensure purposes, however. To use an imperfect analogy, a physician assistant might acquire a very high level of skill and proficiency in a particular area, but their skill in x area cannot be the basis for an unrestricted medical license. Unlike certification, licensure is fundamentally permissive, and that's why the least restrictive licenses are given to those with the highest and broadest level of training.
My point is that we have some idea of what kinds of minimum competencies go along with an accredited doctoral program, whereas master's level training has not been subject to the same kind of standardization, which makes licensure and scope of practice issues difficult to sort out. APA has decided to get into the business of accrediting master's level psychology programs only very recently, so we will likely see some changes down the road.
