Just to be clear here, this problem has been solved -- I'm just looking for an explanation as to why.
I have a design which uses the [Paper] swatch on several objects. I originally noticed the problem when I exported to PDF, opened the file in Acrobat Reader and printed it. Instead of knocking out the [Paper] areas, the printer laid down a light grey color. Thinking that it was an issue with exporting PDF or maybe with Acrobat Reader, I tried to print from InDesign, with nearly the exact same results (slight color variation). The issue then became more complicated when I opened the PDF file in Illustrator, and against all expectations it printed correctly.
I Google'd the topic and was not able to find a direct reference to anyone having this problem. However, I followed some advice I saw for problems that sounded similar. I went to Adobe Bridge and enabled ColorSync. At this point, the print still came out incorrectly. The final step that changed things, however, was when I went to InDesign. I set it up to print, and I went into the Mac printer settings ("Printer..." button). There, I changed "Color Matching" from the "Vendor Matching" setting to "ColorSync > Auto". After changing this setting, the print came out correctly. I went to Adobe Acrobat and changed the setting in that print dialog, and it worked as well.
My question is, what exactly is going on here? I am glad that the problem is solved, but I don't fully understand why it was solved. What is "Vendor Matching" and why was it giving me bad results?