When overlaying an ArcMap Service on top of local layers or other service layers the background of the ArcMap Service layer is not transparent. The features of the layers underneath the ArcMap Service are not visible, even where there are no features of the ArcMap Service.
Along with map features, the data frame also consists of a background. A color for the data frame background is set within the Frame tab of the Data Frame Properties dialog. One of the options for the background is '<None>'.
A misconception is that '<None>' is by default transparent. It is not. '<None>' is a color with an RGB value of 254 255 255. It is not by default transparent.