The Classic and the Classic Elite (PSI) do NOT have removable center rings on the cap opening inserts. (I think the black band you see is actually the outside of the inner threaded sleeve. The two contrasting sleeves appear to be pressed on.) I have purchased every version of that pen in every quality range with the hope of finding one that allowed for this, but to no avail - I really like the size and shape of the pen, so I have tinkered with disassembly. The only capped pen I have found that allows this other than the Mistral (per Phil's note) is Berea's "Baron" and other knock-offs of the same design.
Good luck with your search.