I don’t think it’s that settled at all, certainly not in 1965. Prineas in 2001 showed that MS progression may occur in the absence of immune cells and inflammation, for example [0], and people have complained of progression even when taking extremely strong immunosuppressants.
While involvement of the immune system seems likely, and certainly most treatments target the immune system, I don’t think causality has been rigorously demonstrated. It has however been a few years since I looked into it.
As an aside, ISTM quite likely that there may be several causes for MS.
[0] https://pubmed.ncbi.nlm.nih.gov/11706971/