In general, in the USA, RefSocs can be independent bodies. They remain part of USAR, and have the R&L committee to help develop standards, promotion criteria etc etc.
My Society, Virginia, detached from Virginia Rugby Union just before it became clear that the American landscape was fragmenting.
In very old days, VRU controlled all rugby in Virginia - Senior Club, Youth, College. In about 2011, they all broke apart and could form their own governing bodies. Colleges, for example, depending on their level, could choose their conference - Chesapeake, Cardinals, or NSCRO; all those bodies were part of USA R, but independent organizations.
RefSoc decided we wanted to be independent so that we could serve all clients equally, and not feel forced to prioritize Senior Club - which was what was left of the VRU - over anything else.
USA R going bankrupt and then reconstituting - which is an essay in and of itself, trust me - just reinforced this balkanized landscape where there is no uniformity of practice across RefSocs.