Well, which is it?
If A implies C and B implies C, does it follow that A = B? Not in this universe.
Example: all dogs are mammals, and all cats are mammals, but dogs ≠ cats.
Another: all 3rd outs at 1B prevent runs, and all 3rd-out force outs prevent runs, but 3rd outs at 1B ≠ 3rd-out force outs.
Minimal familiarity with the definition of 'force play' should make it obvious why retiring the BR before he legally touches 1B cannot possibly be a force play, whether or not it's the 3rd out.