I must depend on your location. Here and in Florida, the ones who one businesses that specialize in equine rehab are veterinarians.
They may hire technicians, but I only know of one (out of 9 clinics) where the technician does any actual rehab. And that is mostly hand walking, hosing off inflamed areas, or applying liniments. All the grooms I know are skilled in various massage techniques and myofascial release. They also are good at treating soft tissue lameness (muscles and tendons) and at bringing horses back from injuries of that type.
I can do ultrasound (therapeutic), address pressure points and e-stim. I will only do it if a vet signs off on my plan. Too much liability otherwise.
I do know of a few people who run barns that offer lay ups and legging up. I don't know why there is a need where they live.