Yannick:
I have always put the fringe in the cavity for it seems only logical for maintenance and playability reasons. I think your 1st super is kidding himself...he will still lose green space to green creep over the years and I believe, from experience, that he will be able to manage his putting surface better with the fringe built with the same profile, and serving as a buffer to some degree as opposed to being right up against who knows what in subgrade material IMO.
During construction I have always figured my putting surfaces a bit larger to include the fringe and back it out during the grow-in process. As you know, a lot can happen
between the interface of green cavity and the surrounding subgrade soils. This issue becomes more of a potential problem with clay soils, probably most of what you and I build in, and much less of a concern with sites that are mostly sand where the putting surface materials are very similar to surrounds.
I do agree that it pushes costs a bit higher, but I believe the costs are justified and relatively minor in reality based on the long term play and maintenance benefit.