I served as a protocol therapist when I was in graduate school for an NIMH funded treatment outcome study involving the delivery of cognitive therapy and 'computer-assisted' cognitive therapy as treatment conditions. At the time (while working on my doctorate), I would have been considered a 'masters-level' therapist (as would a social worker (LCSW) involved in the study). Importantly, we were all trained to deliver exactly the same protocol treatment (an abbreviated nine session protocol to treat depression using Beckian cognitive therapy). It was, essentially, a 'manualized' protocol with close supervision, review of our tapes, ratings on session content as well as 'quality' of the session (rated via the Cognitive Therapy Scale). Each therapy session was 'mapped out' in terms of what we were supposed to cover with the client, how we were supposed to cover it, and in what sequence. Also, because it was a treatment outcome study, it had stringent exclusion criteria for participants (e.g., couldn't be on psychotropic meds, couldn't have had a prior course of psychotherapy, couldn't suffer from major comorbidities--e.g., personality disorders, substance abuse).
In the vast majority of treatment outcome studies, there is a tendency to utilize (a) manualized/homogenized treatment protocols, and (b) shall we say, 'simplified' clientele (as described above) to be treated.
It's not surprising that post hoc analyses (by therapist degree, that is, 'masters vs. doctoral') tend to show no differences in outcome related to therapist degree.
However, I don't know that this necessarily 'proves' that it 'makes no difference' whether the treating clinician has a doctorate or a masters degree. One of the biggest differences I see (anecdotally) in practice is a difference in differential diagnostic acumen between the average clinician with a doctorate vs. the average clinician with a masters degree. And the importance of proper differential diagnosis and case formulation in promoting better outcomes seems paramount in clinical practice.
I admit that I haven't looked at the empirical literature that purports to address this question of 'equivalence' in outcome in therapy between doctoral and master's-level therapists, but I think that the methodological realities (that tend toward 'homogenization' of delivered treatments) that are prevalent in psychotherapy treatment outcome studies (that I have described above) are quite pertinent to the interpretation of any such research data.