There is evidence for that correlation, trust and outcome, but why do they trust me is a bit harder to get at. Also, my emotional expressiveness, body language, eye contact, voice tone, etc all play a role in the treatment. These are difficult control for and separate out and there are a lot of other variables. My cultural background and experience and their cultural background and experience, gender, appearance. Sure we could look at trust but it interacts with many other variables. Technique, experience, my age and their age, client's ses, my personal beliefs, clients beliefs. I could go on for days. We can examine all of these things in various ways, but it is extremely difficult to sort it all out. We have different research strategies for this and each methodology has its own limitations and strengths.
Psychology is the study of the mind which is in itself a psychological construct that cannot be directly observed bit can only be inferred based on observed behaviors. Because of this Skinner said that we should ignore the mind and study the behavior, others focus more on what the person reports as being key. CBT tries to integrate both aspects to an extent, but due to emphais on experimental design can still be too reductionistic. Other theoretical approaches tend to be flawed by not having enough testable hypotheses or research behind them. I conceptualize from an object relations stance and there is a lack of effective treatment research in this area unfortunately. Good developmental research on much of it, but not directly connecting how to take that info, guide treatment, and measure outcome. I can talk about this stuff all day long as you can probably tell.