I'd say fading black as well she could be a really dark brown though. Also I just wanna say I love this horse's build before I scrolled down to see all the pics I was thinking Barrel Horse! Posted via Mobile Device
Sorry :)...I go with dark bay. She has the black points on her legs (black below the knee), black mane and tail. In the first pic you can see the color change going down her legs...very dark brown, nearly black on top but there is a definite darkening lower down.
Dark bays do not always fade. I had one that faded into an almost chestnut color; I actually put him on a coat darkening supplement. My last horse, also a dark bay, didn't fade at all.
Really won't know for sure until you do a DNA test. I suspect either fading black or a really dark bay with a lot of smutty. If it was brown I would expect light points around muzzle and other soft areas which I don't see - other than sweat lightening on the neck and back.
As to vets and color - most vets aren't even aware that "brown" is an acceptable color option. It used to be either bay or black. Their main priority is the health of the horse rather than its color.