If it resolves (or even improves) on supplementation then it wasn't true stringhalt. What causes the confusion is that there are a number of other conditions which have similar symptoms.
Australian stringhalt (which is a true stringhalt ) is caused by poisoning and can resolve successfully - although it often doesn't and resolution can take years. There are supplement recommendations for this - usually Vit E although some practitioners reccommend B1 or Thyamine. I can't find any peer reviewed research to support this though.
True stringhalt arises from nerve damage and although surgery to cut the lateral extensor tendon can assist there is nothing you can feed which would help once it has developed.
Conditions which can look like stringhalt but actually are something else include things like upward fixation of the patella. Some degenerative hock issues and occasionally even a foot abscess. Those may resolve either pontaeously or on supplementation.