Ok, I believe I found what was causing this...and it has to do with color MANAGEMENT. Turns out that my brochure (into which I was looking to place the graphic) was assigned to a U.S. Sheetfed Uncoated color profile. However, my black square in Illustrator was assigned to a U.S Sheetfed COATED color profile. I would not have normally looked here for this type of problem but it occurred to me to check this out today and lo and behold that was the problem.

As soon as I assigned the black square in Illustrator to the U.S. Sheetfed UNCOATED color profile (again, same as my brochure in InDesign), and then I placed it in the InDesign doc, everything worked fine.

I never realized that profile differences could force a grayscale image to appear as 4 color within InDesign. Maybe this isn't supposed to happen and it's a bug -- I don't know... but for anyone else out there experiencing this problem, check your color management settings.