You Make the Call!
Photo 5 shows some ingenuity by the installer. He used the existing metal in conjunction with the wall base requested by the customer. But photo 4 show that, at the time of the inspection, the coved areas are no longer adhered. Coving in this manner would not be acceptable to most manufacturers.
Photo 6 sheds a little more light on the installation. It appears that the original (prior to the first and second perimeter) felt-back vinyl was not completely removed. The face and interior foam layer has been peeled off the backing, with the majority of it still adhered to the subfloor. The last time I checked, this would not be a recommended technique for installing felt-backed or perimeter solid vinyl.
As my father used to say, don’t get creative, do it by the book and cover your…posterior.