Hi Alan,
Tables without borders have no borders. A white border is still a border even if does not print.
The "border" in Word jargon is the visible line in the printed table that is between/around cells in a table. A white border on a dark printing background will print as the absence of that color.
Here is a
temporary link to the file with those tables.
It is also possible to have viewing of gridlines turned on in Tables. Those will show on the screen even if there is no border.