Filesize

There is zero difference in a document that is 1000x1000 pixels (as an example) at 72 dpi (PPI) or 720 dpi (PPI) or any such value. All are 1000x1000 pixels and the dpi/ppi is simply a metadata tag. 
This very, very old primer on resolution still seems necessary to post, this may help in understanding what the printer clearly doesn't by their request:
http://digitaldog.net/files/Resolution.pdf

First don't confuse PPI (pixels per inch) and DPI (dots per inch). They are not the same, one does not imply the other. You can choose to export at a certain PPI (not DPI), but in most cases this is meaningless. It has no impact.

Digital images are measured in pixels, not pixels per inch, as they don't have inches.

So if you export an image that is 6000x4000 pixels, it is exported at 6000x4000 pixels, regardless of the PPI, which is essentially meaningless.

PPI (not dpi) is resolution for printing, and doesn't affect the file size.

If you have a 6000 x 4000 px image, at 100 PPI, it will print at 60 x  40 inches.

At 1200 PPI it wil print at 5 x 3.33 inches.

Pixel dimensions divided by PPI value = Printed dimensions in inches.

The real resolution of a digital image is the pixel dimensions.