According to all your logics Gretsch and camco and Rogers were jasper shell decorators just trying to see the logic.
Actually, VM2K stated, "My take on an assembler is just a person that buys a shell blank, from say Precision drum co, or Drummaker or a custom maker etc and has them do the edges, snare beds and all appropriate holes for the necessary hardware."
Other than building their own shells, Gretsch (for a time period) and Camco fall into his definition of builder. "...cuts the bearing edges and the snare beds, and all the necessary holes to hang all the appropriate hardware to the shell." Gretsch has the shell provider build a very specific layup that is unique to Gretsch alone.
Most of the companies outsource lugs and hardware.
Where does that leave Rogers???
The definition variance is a pretty tough thing to pin down.
Not quite sure where I stand on this. I believe I'll ruminate on it for another 45 years or so.