1) Given ~1M vets, ~800 diagnosed with MS after having 2-3 blood samples taken. Of those, most without EBV exposure didn't get MS until they were exposed. MS is rare (<1%), and EBV is ubiquitous (>95%?), so getting large numbers of unexposed people who get MS would be hard in any case. It's unclear if they corrected e.g., for expected age of onset (~30) since I expect they started sampling blood in ~20 y.o.'s.
2) Some researchers claim molecular mimicry, where an EBV protein looks very close to a protein on the foot of myelin (near the edge)
But in MS it's not clear if the inflammation causes the myelin loss or some nerve pathology causes the loss (which causes the inflammation). There's a line of evidence that the axons are disrupted well before the myelin loss.
Also, MS is a clinical disease: it's just "multiple" "sclerosis" in the CNS -- without other more specific causes like MOG/NMO. There could be many causes that end up creating multiple demyelinating plaques, so EBV, even if it is a cause, might not be a principle one.
Finally, the problematic form of MS is the (typically later) progressive phase, with increasing disability even without immune flairs. While some immune suppressants can limit the (earlier) flairs, drugs approved for progressive are barely better than nothing.
Also, the incidence of MS seems to be increasing overall. sigh.