If I understand correctly what you guys have said your Medicare and Tricare are just health insurance. The Workers Comp would cover you if you got hurt on the job and it will cover the medical bills that go with that injury plus it should pay you time loss benefits (cash) for the time you are out of work because of the injury.
Any payments for any time lost (compensation recovery) depends on if you are an employee, not a contractor. In the case of being a contractor, it won't cover any loses because you are a contractor and in this case you are in control of what the company can tell you what to do.
I agree with Greg. I had an accident in Ohio on 9/2/09 and went to the ER for xrays. The W.C. paid only the medical bills. I was off work for three weeks but did not request to be paid for that time. I was still sent a denial of pay by the Ohio WC board They stated that I was not elegible due to being an indepentent contrator.
It depends on your home state and the domicile of your carrier. State laws vary from state to state. You are probably smart to have work comp or occupational accident insurance either way. As an independent contractor you are generally your only source of income. Covering medical bills is important, but protecting your revenue stream is probably most important in the long run.