iOS 10.3.1 - Apple iPhone - Photos app shows 295 images; none found on device internal storage
I have no explanation for how the photos came to be read-only on the device, and hidden from the internal file system, but the solution to make a backup was:

On the device, navigate to the album. 

Select All images, then choose 'Duplicate to Edit' which places copies into Camera Roll. 

Once the duplicates are created, any of the usual methods for backup worked.

In my case, I could plug in with USB cord to my Windows PC, and transfer using Windows Explorer by navigating to iPhone\Internal Storage\DCIM\XXXX.