If you are leaving the 72 PPI in the resolution box and then resizing the print size in inches down to say 3 X 4 inches you are losing most of your pixels and the publisher is right. Almost any decent software that will crop and resize your images will have a “Resample” box – DO NOT CHECK IT or you will lose most of your pixels.
Print size doesn’t really have anything to do with the size of the image in pixels unless you check “resample”, leave the 72PPI and downsize the print size. Then it dumps pixels. If you don’t resample and downsize the print size your PPI will go up as it keeps all of the pixels and applies them to a smaller print.