They get paid by the person driving the truck. It is Fedex who dodges them.
They don't dodge them. They have to pay enough to make it worth it to the drivers net of taxes. If they paid the taxes they would pay the drivers less. Since the total taxes paid in the transaction are the same either way its hard to imagine tax avoidance is the motive.
In my business experience, when a worker is labeled a contractor and treated like an employee, it's always a tax dodge. When a contractor is really a contractor, the tax burden is more equitable.