I don't believe a vet is a necessity, unless - god forbid - it has progressed to infection of P3, lateral cartilages or such, or it is so deep and broad that it needs major resection. You're correct that it's like thrush, just that it affects unhealthy wall material where thrush affects unhealthy frogs. It is a name for opportunistic infection & can be fungal or bacterial.
As Trinity said, it is usually necessary to cut away infected wall material(resecting), unless it's obviously shallow/superficial, so hopefully the farrier already did that when he 'diagnosed' it. He should have also advised your friend about follow up treatment to kill any remaining infection.
Being 'opportunistic' meaning it only infects already compromised capsules, along with the 'first aid', overall hoof health, mechanics, diet & environment need to be addressed too.
Thank you for such a concise definition of what White Line is! All the Googling has been rather alarming.
I don't think it's progressed that far (I really, really hope not) Sera is not lame, and the farrier (to my knowledge anyway - I wasn't there) did not say it was at that level of infection. Heaven forbid.
As for the vet, I'll leave that up to her, but share what I've learned. This is her first horse and she's already had quite a scare with a pretty bad colic! Although, even if it were not, I can understand her alarm.
Sera is sound and shod on all four feet, but does have a minor club foot, which is the hoof in question. She relatively recently developed a small hole on the outside wall (the quarter I think it's called?) where the hoof meets the ground of said back right hoof. Last visit, the farrier had attended to it, but the hole has not gotten better (even a smidge bigger). Pre-farrier arrival, on a ride, we noticed Sera occasionally hit one hoof with the other. The hole, we thought, now may have an explanation which we hoped would be confirmed by the farrier. Bell boots added to my friend's shopping list. Then the farrier came the other day and the White Line was found. I've not been out to the barn since (pouring rain here in LA! Drizzle I don't mind..) but plan to go today even if there is a monsoon. Not used to no horse time for two days in a row! When I do go, I'll have a look at Sera's hoof to see if they cut away any of the infected wall material. I hope not! I hope it's superficial!
Thanks so much!