Re-refined oil, I have zero problem with at all. If the end product meets original specs, it meets original specs.
I checked into a waste oil burner to heat my shop, but it would have to be code compliant, EPA compliant, etc or my homeowner's insurance wouldn't cover any issues. If it was just my shop out in the middle of nowhere burning down, I'd probably do it and accept the risk. As it is, if my shop goes, then my house is going too, and likely also several neighbor's out buildings and fences. I want the insurance coverage, and will decline to do anything stupid out there.