I'm a bit confused- was this advice from the neurologist or her GP?
You could point out what most of us know, but often ignore- namely that doctors are no smarter than anyone else and have their wierd beliefs and biases just like the rest of us. You could ask her to ask for evidence.
It might also be worth asking your daughter EXACTLY what was said by both parties.
(People tend to miss a lot of details out when they report conversations to a third party). Is it possible for instance that she said something like "Would it be worth seeing a naturopath?" and he said "It couldn't do any harm to try?" - which is functionally the same as advising her to see a naturopath, but actually may just be a bloke with no idea what a naturopath is , just waffling.
If the doctor feels the headaches are psychosomatic in origin, stress related, whatever, he/she may feel the placebo effect of seeing a herbalist might actually be enough to help - on the basis that anything that relaxes your daughter may help. He might as easily have suggested long walks in the countryside or taking up yoga. He may feel that if it does help, that would be supportive of a stress diagnosis.
A lot of persistent headaches seem to be due ultimately to stress, manifesting through things like muscle tension, bad posture and the like. If he has failed to find an organic cause, he may feel that what's needed is to make your daughter feel she is "taking control" of her problem. I'm guessing here.
I know schoolteaching can be a chronically stressful job. My guess- and all the usual caveats apply- would be she doesn't get nearly enough relaxation time. Take up yoga? Walk at least 30 minutes before bed? This sort of thing sounds banal, but is easy to try and just might help- and this may be what he's really doing, trying to divert her behaviour to see if it helps the chronic problem.
There are fads and fashions among doctors, who are part of our shared culture after all. Thirty years ago he might have advised seeing a shrink.
I do know one GP who regularly advises patients in a certain group (mainly female aged 50-70) to visit an aromatherapist masseur. His reasoning is that this group of patients appear in his surgery frequently- sometimes weekly- and appear to have absolutely nothing clinically wrong with them so far as he can see. They tend to be single, childless, or mothers whose kids are grown, and a shade more health obsessed than is good for them (his words, not mine). There is absolutely nothing he can do for them clinically, but he has found they mostly report feeling better for the aromatherapy thing , and he sees a lot less of them. So from his point of view he actually is helping them.
Maybe this doc just happens to know a naturopath. I'd be concerned only if I found he was recommending a specific practice which turned out to be his wife or someone.
On balance though, I think I'd try the long walks or yoga first- either should help any cause that a naturopath could help and they would be cheaper and probably safer, though I suppose there's hazard even in a walk, particularly for a woman alone. Nothing is totally risk free.
