I am integrative, and think I can discuss how so in a manner that addresses erg's points, which are excellent... but be forewarned, this is a rather lengthy post.
A therapist CANNOT be "integrative" if they do not have a strong (very strong) grasp on the theoretical orientations that they draw from, including how to accurately conceptualize cases and implement interventions or techniques, or everyone's concerns about them B.S.'ing and flying by the seat of their pants is completely warranted.
My initial training was in family systems and client-centered therapeutic styles. During my Masters I interned at a college counseling center and a co-occuring substance dependence/mental health treatment facility. Family systems wasn't a helpful conceptualization or skill set for most of the presenting problems I worked with, and client-centered therapy techniques weren't tangibly helpful enough when it came to working with many of the disorders people were presenting with, including anxiety disorders such as panic d/o. Some of my supervisors clearly gave me training and supervision in using CBT for panic etc. after some failures with using the approaches I knew.
This is when I became a therapist who utilizes empirically-supported treatments. I was infuriated that any supervisor would allow me or have me use anything as a first approach that had no research backing as effective for treating a set of symptoms. I started attending trainings and getting CEUs in ESTs, reading more journal articles, psychologicaltreatments.org, psychotherapy brown bag... any and every resource I could on IDing and learning ESTs. Then I decided to continue on with school (rather than sticking with a terminal Masters) and chose a strictly CBT school, where I have intensively studied Cognitive therapy, Behavioral therapy, CBT, and some second and third-wave (but heavily CBT) approaches such as MI and Problem-Solving Therapy.
However, since my passion is working with complex co-morbidity between mental health, physical health, substance abuse and anything else under the sun, I have experienced the shortcomings of CBT. It can be rigid and inflexible (which at times is absolutely necessary/critical to the proper implementation of an intervention, like Prolonged Exposure and other exposure protocols such as EXRP... but at times is off putting to the clients), cold and/or impersonal (I've heard from clients, mostly related to its standardized format), and protocols technically HAVE to be integrated with a clinical rationale and strong enough research backing for any true co-morbidity, as so many studies on interventions isolate 1 disorder (this is easier for certain co-morbidities and more challenging for others). Then there's always the tricky part of the people who don't respond well to CBT or other ESTs, or who could be considered "treatment resistant," etc... or who have very chronic cases...
This realization is when I started receiving training and supervision in Acceptance and Commitment Therapy. I was an extern in a behavioral medicine placement working with persons with chronic and severe medical conditions, some of whom also experienced chronic serious mental health conditions as well as substance use disorders. Several of the supervising psychologists implemented ACT, so over the course of this last year I received training and supervision in it and Relational Frame theory, the empirical support for it thus far, etc... and it has completely revolutionized my practice. I've seen it be effective with several clients who were hitting walls in CBT, and have seen it tie together the overall treatment of co-morbid cases where one disorder was receiving primary intervention while others took a back seat for various reasons.
In order to do this well (back to erg's point and concern), I have to clearly conceptualize this person's presenting issues through the lens of the research, meaning what treatments are supported, which EST case conceptualizations appear to fit the client, and what conceptualization do THEY SAY fits them? Then ongoing review continues to dictate if the approach is being effective, as well as whether any alternative conceptualizations (that have empirical support) add to or potentially explain barriers. Again, this is discussed with the client, and at times additional theories are introduced (whether that is MI regarding a certain problem, developing communication skills or assertiveness, or incorporating ACT and ACT consistent approaches).
IF the treatment interventions are not consistently anchored in the research and a strong case conceptualization that is confirmed by the client, then the therapist is either flying by the seat of their pants, guessing, sticking with what they feel comfortable with, or making some type of assumptions. I also emphasize that however progress is measured, it must be measured on an ongoing basis to help both the client and the therapist know if they need to switch gears (which a therapist can do if they are well trained in multiple approaches, know their stuff, and have supervision and/or consultation) or refer.
To me, that is a responsible way to do therapy on multiple levels, and the best way that I can define my "integrative" approach to therapy. Admittedly, I my theoretical orientation is CBT first or as the core/basis, branching out from there. I honestly don't care what other therapists' core orientations are as long as they are ESTs.
Did that help anybody? I feel like I just wrote my theoretical orientation essay for the APPI.
Oh and lastly, if I were to see a personal therapist, I would absolutely see someone who practices from an ACT perspective. I'm applying a lot of the interventions to my personal life and am seeing personal growth and changes from it. However, the ADHD/grad coach type psychologist I see is very CBT. I definitely need the skills development emphasis there... but I wouldn't for personal therapy.