I think the concept is meaningless in the whisky world. A distillery is a distillery is a distillery. All are beholden to shareholders (whether public, private or sole owner in the case of Bladnoch). All have an objective of maximising profit, whatever they may say. All will cease trading if their losses are too great.
In the brewing world, CAMRA invented the term "small independent" as distinct from "national" - and they defined six national groups and painted them to be demons producing bland beer. Eventually legislation came through to restrict big brewing companies, with a result that some of the bigger companies slimmed down and some of the smaller companies fattened up. The terms "national" and "small independent" are now still used, but in ever less meaningful ways.
I guess many people will try to create a definition of independent in the whisky world that includes Bruichladdich but excludes others for reasons that I don't quite understand. If the definition that people choose is membership or otherwise of the SWA then so be it. Ideally, though, distilleries would all agree on definitions and labelling whether or not they were members of the SWA. Personally, I will judge distilleries on their output and, I'm afraid, some of the "independents" probably ought to concentrate just a little more on making their whisky taste nicer.
By the by, the non-members strike me as being a bit like the non union members at work who proudly proclaim their independence, save on the subscriptions, but benefit from the union's collective bargaining for terms, conditions and pay.