Konqueror does it, as file manager or web browser.

For me the texts File -Edit - View - Bookmarks - Tools - Settings - Help
display as a clashing brown colour with white text. I have extensively searched the KDE Control Center -> Appearance & Themes, explored K-> Menu_Editor, and there seems no way to alter the thing. Type-in menu text entry boxes outline in the same colour when in use.

I suspect it migt be some kind of GTK or Gnome compatibility theme in there somewhere, possibly in a hidden file, but I have not the knowledge to dig it out quickly.

Does anyone know how this is done?

In my KDE (3.5.2) this sort of stuff is set by
K-> System Settings -> Appearance -> Colours
You can choose a predefined colour scheme, modify it, or create your own.
With KDE 3.1.0 it is under
K -> Configuration -> KDE ->LookNFeel -> Colours

If you are really stuck, rename your /home/gtrax/.kde to .kde_badcolours
logout & login again. You will be back to the defaults for your installation.