My husband is a floorcovering professional and he says they are totally wrong. They could have left the old vinyl down but they should have scraped off the loose material and then used a product called Ardex Featherfinish or self leveling mortar to smooth out the surface prior to installing the vinyl. If you are willing to live with the vinyl you should certainly hold back payment. However, in the end you have a new floor you will always look at with disgust. Make them do it right and replace it or do not pay them is what he suggests. You have not added value to the home and when you go to sell it, most likely, the new buyer will feel they need to replace the vinyl and want to offer you less for the home.
HTH,
Lisa