Similary, when we send a photo to our Canon or Epson, there is ZERO correlation of an embedded dpi value (if the EXIF is present) with how many dots of ink per inch are emitted by the printer.
Well for printing, PPI of image does come into play. As my link's example shows with the same pixel dimension of an image of a kitty: it can fill the printed paper at 72DPI and be smaller then a postage stamp at 1000 DPI. If the printer could print a true 1000 perceptual DPI, then that kitty would look good with a magnifying glass! The old standard of printing was that an image that had a native density of 300DPI was good for viewing at close distances. You could go down to 150DPI if it was for posters (where viewing distance wasn't as close), and then you can have a really small DPI for billboards. Now current photo printers have non-rectangular dot patterns, but usually are processing at 600 PPI. If you're printing for the greatest quality at very close viewing distance, then it's best to have a source resolution that can fill your intended dimension with native PPI. If the PPI is lower, the printer is doing its own re-sampling. You may or may not find a better re-sampling algorithm with Photoshop.