Does an employer in Texas have to provide workmen's compensation insurance for an employee if that person has their own private insurance?

Texas is the only state were an employee does not have to have workers' comp insurance. Instead they can have a private accident insurance plan. But they must have one or the other. AN employer can exclude contract employees from coverage under their plan (at least in Texas). I forget the exact number, but I know if an employer is a small company, I think it may be under 15, then they don't have to have workers comp or an accident plan.