Once the cupping wear has got to the stage of causing vibrations that you can feel as you ride, even flipping the tires on the rims & trying to 'wear' the cupping out by running them the other way around isn't going to stop the vibrations (altho if you flip them early enough, you can sometimes even out the wear & then fix the wheel alignment/tire/pressure issues causing the cupping) So the tire dealer is right in not wanting to balance them, that wouldn't really do anything for you or the tires, except make you think he'd suckered you into spending money on doing pointless work!!
But Chupaca is right, there's no point in fitting new tires without fixing the issue that's caused the cupping/wear first, & that cause is most likely going to be poor wheel alignment &/or incorrect tire pressures, possibly compounded by running crap tires.... :sour: