You are right...there must be clear etiology and documentation for IVIG to be approved. This is one of the reason I suggest people get the skin biopsy as it's typically required for approval of this treatment.
That being said, I have Medicare (who rejects treatments frequently) as my primary insurance and it pays for this for both my immune deficiency and treatment of immune mediated neuropathy. So it is possible to get this treatment...but those in the UK will find it much harder.
The exact mechanism is not fully understood...as you'll read in this article. But IVIG is like an immune modulator and helps to organize the immune system for better function (when autoimmune diseases attack the body). Once the attack is no longer against the nerves then I guess they can start to heal.
http://www.medscape.com/viewarticle/730670_3