Why do gray axles appear black and black axles appear white and black in this manual?
I don't have this set, but used 8421 as a test. This set is also released in 2005.
Looking at the PDF you see the same color scheme of the axles, were the black appear to be gray and vice versa

When looking at the instruction manual

You see the normal colors, so indeed your set came with the normal colors and due to some bad scanning and compression the pdf got discolored