First off, the question that brought me to this thread:
More to the point, though -- let me guess, you've printed it on laser and found the disgusting dither pattern because Altium's default sheet is just slightly off white? Yeah, I fixed that shit long ago on my templates... 
How do you do that?? I can't find any settings for the background color for print/PDF output. (Just the settings for the on-screen schematic editor.)
Err... huh...
I mean, I don't think there's such a thing as through-page transparency in PDF. Objects on the page, maybe?
Old, I know. But actually, yes, PDFs
can have a transparent background, and it's VERY handy in some situations, like if you need to extract a vector graphic out of a PDF into some other program, or placing a PDF as a graphic into another document. (This is fairly rare on Windows, but surprisingly common on the Mac.)
Another theoretical use (though I have no idea whether PDF is used for this in practice) is for printing T-shirts and window stickers, where they do, in fact, have white ink as a separate color.
It's not impossible to suppose that one could actually format a page this way. The printer would know what kind of media to use, based on the background: a 100% transparent background would be printed on acetate, a partial transparency might be printed on matte (translucent) stock, an opaque background on paper or other; etc.
But, I don't think this is done at all, and so, what's printed, is always an additive pigment (subtractive color) process. And for that, by definition, white is the absence of all color, yup.
Well, no. That's how office printers work. But once you get into commercial graphics, it's not at all unusual to have opaque spot colors to work with, including white ink or metallic films. (Or even surface-modifying coatings: back in the 90s, National Geographic had a few years where they used gloss lacquer as a spot color, selectively applying gloss onto parts of the page. Glossy black on matte black is a fascinating and elegant effect.)
Modern commercial UV-cure inkjet printers (the type commonly used to print rigid boards, phone cases, etc.) often have CMYK plus white, specifically to enable printing white onto transparent or dark substrates. (The CMY inks can be transparent or opaque.)
(Not to be patronizing, if this is a misinterpretation of your intent -- rather, just to entertain the thought of a document format that supports transparency literally everywhere.
)
That's a very, very common thing actually. Most people just don't realize that when using such formats, their software is usually drawing or specifying a white background for them!