We live in Japan and frequently have occasion to visit Kobe for work. Kobe is a really hard place to find good food at and this place has saved us on numerous occasions.
As noted by another user you will need to make a special request to ensure your food does not contain fish broth. We speak native level Japanese and one of us is native, so whilst I can't comment on the experience of the other user re being refused, I know it is definitely possible to eat well here as a vegan, with a good spread of different vegetable dishes cooked in a healthy, typically Japanese way. You will need to be polite and unassuming though and know that they don't generally speak English so some sensitivity and effort will not go astray. Good luck!
Cons: you need to make a special request, English probably not spoken