Previously I had been Googling for "PNG pixels per inch" and found nothing. But with the clue that the data was in meters, Googling for "PNG pixels per meter" yielded this:

Earlier Adobe versions (prior to Photoshop 7 or Elements 2.0) did not store or read the ppi number to scale print size in PNG files (Adobe previously treated PNG like GIF in this respect, indicated 72 ppi regardless). The ppi number never matters on the video screen or web, but it was a serious usability flaw for printing purposes. Without that stored ppi number, we must scale the image again every time we print it. If we understand this, it should be no big deal, and at home, we probably automatically do that anyway (digital cameras do the same thing with their JPG files). But sending a potentially unsized image to a commercial printer is a mistake, and so TIF files should be used in that regard.

Most other programs do store and use the correct scaled resolution value in PNG files. PNG stores resolution internally as pixels per meter, so when calculating back to pixels per inch, some programs may show excessive decimal digits, perhaps 299.999 ppi instead of 300 ppi (no big deal).

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)