Despite what some (including certain elements of the CAA) would have you believe, the privileges of a JAA CRI rating do not extend to differences training. According to Schedule 7 of the ANO, "A class rating instructor rating (single-pilot aeroplane) entitles the holder to instruct licence holders for the issue of a type or class rating for single-pilot aeroplanes."No more and no less.
I followed this up after our last discussion on this and have in writing from flight crew policy that a CRI can indeed teach for all differences training and is not restricted as you suggest. That is your interpretation and the Official policy is fortunately different.
The majority of LAA coaches are also CRI's with the remainder of us being FI's and Examiners.