In the Inspector, select the appearance tab and turn off the borders for these fields. That should leave you with just the inner box.
Ahhh ... while in the Inspector the border shows up, but when back to the layout it does go away -- at least until it is selected, then it re-appears. Also noticed I cannot seem to get the halo of the Fill from not showing up .. the fill from inside the box gets transferred to the fill of the entire box, so with the border off, you still get the Fill surrounding the box -- a halo effort .. kind of annoying but much better.
Anyway of getting a Filled box and a transparent background --or the inside of the box to take on another color other than Fill -- they seem to sync up in FMP 11 that is ... Thanks
The field can be set to be transparent and you might check and see how the layout looks in browse mode when you disable "Show Field Frames when record is active" in layout setup...