Hey Walt, here are a couple of photos which exhibit the problem. They were taken on an S7 phone. They're zipped so they don't get modified by uploading here, and you can experiment without altering the originals.
NXT 7's Slideshow Assistant rejects the one straight out of the phone, but accepts the other which has been re-saved. Here is a screen-shot of Slideshow Assistant a couple of minutes ago. That is NXT 7, but the photos are behaving exactly the same as they did with my NXT 6 last year.
Yes, the Samsung agent is wrong. Can't blame him I suppose, they're telephone answerers not technical people. The S7 photos do contain Exif data and if you load them into a (non-Roxio) photo editor and then re-save them, the Roxio programs will accept them going forward.
The dates on the screen-shots you posted - That isn't a new direction to look, it just confirms that the Roxio program can't read the S7 Exif data properly. There are two ways to store numbers in Exif and Roxio gets the numbers back-to-front.
There is no point in your paying to get NXT 7, since it behaves the same way as NXT 2, 3, 4, 5, and 6 did.
Viewing photos: They've taken away the old Windows Photo Viewer from Windows 10, but if you right-click a photo and look down the options available you should see "Open With", and going right from there you should see "Paint" among the selection. If you open a copy of a rejected photo in Paint, and then save it again, the saved photo should be accepted by Roxio. (I suggest working on copies while you get this sorted, so you don't overwrite the originals)
Whew! Did I answer all the questions?