After posting that, Paul ('pakt' in the Puppy Forum) sent me a message that the maximum current capability of the USB sockets can be increased from 600mA to 1.2A by doing this in the 'config.txt' file (in the vfat first partition):
I am happy to report that both of these drives work on my Raspberry Pi3. I copied a 1.2GB file to and from, and md5sums were correct.
This is very good news. There is a 314GB PiDrive that has been especially designed to work with the Pi. But, why buy that when these very cheap 1TB drives work? A cynical person might think that someone thought up a bright idea to get rid of some old stock of 314GB drives.
On the otherhand, the PiDrive might be required if you have a less capable power supply.