To go a little bit further with the explanation is that in order to get white when printing on a color paper you have to print with white ink of some kind. When you use white fill in Illustrator in a CMYK document what you are telling Illustrator to do is not let the underlying art show through the fill of that white filled art.
If you want white to actually print such as with a flexographic or silk screen process then you would create a spot white swatch. But if you are printing offset or inkjet or an rgb device then white is no color as opposed to know fill since there is no white ink being applied and the color of the paper is not white.
Just in case you did not realize there is no way to make white on a colored paper other than to actually print a white ink which is only done in certain specialized printers.
But if you need it on say a cover of a brochure the process usually used is called Hot Stamped or you can use Silk Screen. It is not terribly expensive if you are doing one color.
They do now have some inkjets that can print white inks.