Yes, and no. But it depends.
Panther doesn't get a cut of the premium.
But as for worker's compensation, if you get actual worker's compensation, instead of Occupational Accident Insurance, then you'll pay the same as an employer would, depending on how many worker's comp claims the employer had over a given period of time. The more claims the employer has, the higher their premiums.
I pay $17.47 per week for my Occupational Accident Insurance. Comes right out of my settlement, shown as Occupational Insurance.
In Ohio, I'm not sure (and someone will hopefully correct me if I'm wrong), but I think it actually is worker's compensation, where you are self-employed and you are your own worker, and thus will need worker's compensation. In many states, like Kentucky, you cannot get worker's compensation on yourself unless you are an actual employee. Self-employed and independent contractors are not eligible for worker's compensation in Kentucky. In that case you need Occupational Health Insurance, which is essentially the same thing as worker's compensation, where it pays for work-related injuries. No lost wages are paid. The policy can be set up in effect to be disability insurance, as well, which will pay lost wages, either in addition to or instead of accident insurance.
It's not Ohio law that you fall under, it's the law of the state in which you reside. But you will have to have one or the other, whichever one you're eligible for.