I offer as evidence on this very topic - an original period WW2 German die for a mass produced ring,,made flat. Also a picture from a period book showing regular rings being made in the flat. Both by the way from a metal master..
It is not just for these 2 rings.. I've had to study report/make comment on well over 100 rings,,and all the same..

You want to talk fancy, multi piece with a bunch of embelishments? ,then yes probably cast from a model and soldered up, hand finished,maybe burnished afterwards or gem set in.

As far as Herr Peicl,,either he knew English or the 2 members on this forum knew German because they both ordered the last of the rings he made.. He knows/knew 100% how the HR ring was made,,and believe what you want but so does Don...