I'm pretty sure he's thinking painkillers are classed as psychiatric drugs, which if they were would mean he was correct.
But on your point, personally I think abuse of benzodiazepines is more likely to lead to a drug like Heroin than psychedelics are. The whole concept of "gateway drugs" hasn't been proven, but the effect of benzos is a lot closer to heroin than psychedelics (anyone who has actually tried heroin might correct me on this...), so would imagine a stronger cross-over (even if not due to a gateway effect, simply down to the fact that anyone who likes downers is likely to try other downers).
But on your point, personally I think abuse of benzodiazepines is more likely to lead to a drug like Heroin than psychedelics are. The whole concept of "gateway drugs" hasn't been proven, but the effect of benzos is a lot closer to heroin than psychedelics (anyone who has actually tried heroin might correct me on this...), so would imagine a stronger cross-over (even if not due to a gateway effect, simply down to the fact that anyone who likes downers is likely to try other downers).