Where I went for inpatient treatment, elements of CBT were taught (SMART), the lizard-brain concept was discussed (RR), and LifeRing meetings were available next to AA meetings (but neither were required, just recommended). So some of the concepts were there, but from a medical/psychological perspective that predates Smart and RR (LifeRing really has no program but is instead a sort of philosophy). The place I went before that was much more 12-step based, so it depends where you go.
But yes, I think the main obstacle to greater acceptance of secular approaches in rehabs is the fact that most of the staff are former addicts who went through 12-step programs and don't look outside that box. It might take another generation, but it is getting traction.