I originally posted a long message as to why this is needed and upvoted the feature request. Then, I realized this feature already there. Instead of selecting 'None' for cell borders, select '(Ignore)'. The table border styles will be grayed out. When I did this, the table borders showed over the background color. This allows users that do need to override the table borders (I'm sure there are use cases where this is needed) to set borders accordingly. However, if you want the table borders to show (as I'm sure the vast majority do), leave it at the default setting (grayed out) and it will work.
T. Carano
I originally posted a long message as to why this is needed and upvoted the feature request. Then, I realized this feature already there. Instead of selecting 'None' for cell borders, select '(Ignore)'. The table border styles will be grayed out. When I did this, the table borders showed over the background color. This allows users that do need to override the table borders (I'm sure there are use cases where this is needed) to set borders accordingly. However, if you want the table borders to show (as I'm sure the vast majority do), leave it at the default setting (grayed out) and it will work.