Unless the rules have changed in the last few years the "Generator" is the owner of the waste. The Waste Hauler has a contract to tranport and possibly store it, but I believe ownership (along with its liabilities) are forever attached to the Generator.
Although, if it is recycled into another product, I think different rules may apply. At least that was the way I understood it when it was explained at several EPA Workshops for Manufacturers.
It has been a few years, so the rules could have been changed. It's also possible that my memory is a little fuzzy on this matter.
With all of the fees, fines, and regulations that are imposed on manufacturers, it's no wonder that they are trying to shift operations to other countries.