Yes, I agree with you somewhat.
Green tea (which also enhances your immune system) is something else that is a toss-up in MS. I think the overwhelming evidence between how bad it is for you if you have MS compared to how good it is for you if you have MS, the good outweighs the bad by far!
So........yes, it's a tossup, allright, and a person will probably get different advice from different doctors depending on their viewpoint, etc.
Basically, though, the main reason (whether it is a wive's tale or not) is the "enhancing vs suppressing" argument. Which as your neuro said, can get pretty complex!
EDIT: You definitely want to consider loading up on anti-oxidants in MS, and doing that sometimes overlaps with the adage of "enhancement" of the immune system, so Catch 22. Go figure!