When I saw the title, I thought this was going to be a re-run of a request that comes up every few months, but you have raised an interesting question.
There is absolutely no need for an ASU pilot to hold a JAA ATPL(H), rather than a CPL(H). You do not need an IR nor MCC experience, which is the significant difference between these two licences.
The requirements for ASU pilots are set down in the relevant PAOM. All PAOMs are based upon a standard "Part 1" published by the CAA as CAP 612. In there it says that the min qualification shall be a CPL(H). It then goes on to say that the operator shall stipulate the minimum levels of acceptable experience in the Part 2 of the PAOM. The Part 2 is written by the PAOC holder.
I think that the reference to an ATPL(H) goes back to the "old days" i.e. pre-JAR FCL. The only difference between a CPL(H) and an ATPL(H) then was the different minimum levels of experience. You needed the same ground exams and flight test and no IR. Thus, a CAA ATPL(H) and a JAA ATPL(H) are not the same beast.
I suspect that what PAOC holders have done is specify an ATPL(H) as part of the minimum experience requirements, when they wrote their PAOM back in the olden days. No one has caught up yet to the fact that almost all ASU pilots will not get an ATPL(H) when they renew their licence, but only a CPL(H).
If it becomes an issue in a particular case, you can only raise it and suggest that an JAA ATPL(H) is not needed, and that any requirement should be changed in the light of the changed requirements for an ATPL(H). However, until a PAOM is changed the PAOC holder may well be held to it by the CAA.