Plain skin called "plain" because it does not provide any skinning. No backgrounds, colors and so on.. So you see the designed result You just need to define backgrounds on your own in this particular case.
by the way,
I have a solution, but this is not the best solution as I know. here it is :
to over write the css classes of rich calendar. eg. to over write rich-calendar-button, rich-calendar-input ...
About "it's not the best solution" - Actually it's the best solution. These classes defined specially for that.. In order developers to use them for styling in plan skin or new skin or customizing actual skin styles in any existent.
Thanks Ilya for the useful response