The mouse itself is controlled by the x-server which controls what how each button works. However, the click action is controlled by the window manager.
So you can change the buttons by the x-server (such as if you have a 5 button mouse - the scroll wheel is actually three buttons, forward is one, back is one, and click is the third) such as moving the right to left, or having the scroll wheel be the left and right if you want to get really wild. You can even assign keyboard keys, using imwheel, to mouse buttons (an example is a 7 button mouse with button on each side of the mouse - you can assign Alt + right arrow and Alt + left arrow to make a web browser go back or forward a page).
The window manager in KDE controls what actions take place when you click or double-click the button. That is the one that controls what happens when you double-click on the desktop. If there is not a setting for double-click, then nothing will happen, such as here with KDE.
Imwheel is a fun little program that can help you remap you mouse buttons to use keyboard actions. But a word of caution - the remap works everywhere so if you assign a keyboard combination to a mouse button, it will work everywhere, not just the desktop.
I'm not a big expert on this stuff, and you problably already know a lot of the above, but I do hope this helps a litte.