Hi Will,
That's not the behaviour I'm getting. Here's a screen shot, taken while Show Print view was in effect. The table on the right is a duplicate of the one on the left. Except for being selected, and having different names, the tables are identical.

Note that the light grey fill of the header row and header column is visible in both, as is the darker grey fill I applied to two cells in the original table before duplicating.
Preparing these, I did notice one missing instruction in my previous post; Removing the cell borders requires a two pass process:
Select the block of cells (or the whole table)
Pass 1
- click the border selection button (left of the one showing "thin" in the post above) and choose Outside Edges.
- Click the line style button ("thin") and select 'none'
Pass 2
- click the border selection button (left of the one showing "thin" in the post above) and choose Inside Borders.
- Click the line style button ("thin") and select 'none' (even if it already shows this).
Click away from the table to deselect it and view the results.
Regards,
Barry