I would here differentiate between someone who has become a barn or stable manager, and an FEI show groom (even if the title is head groom or home groom).
That said,
NONE OF THEM ARE INDEPENDENT CONTRACTORS.
Having groomed for an Olympian, nope, it wasn’t an independent contracting position. Even if I could much of the time decide what time I wanted to clean or ride or lunge or clip or whatnot, it was still stuff that had to get done every day. This is equally true regardless of whether one is at home or on the road. My boss being gone for ten weeks didn’t make me an independent contractor.
There are top riders who do employ what I would consider independent contractors, people who work with them for a particular show (we call them freelancers or day grooms), and I have friends who exclusively do freelance work now, I have done this myself, but this is more common for a second groom, rather than a first or only groom, especially when we are talking about top riders and programs. In these cases, employment is usually the length of a particular show or tour. These people I would say could probably legally be classified as independent contractors.
That really isn’t what we are talking about here, to my reading, but instead full time professional grooms for a rider or barn.