I copied the two files "iTunes Library" and "iTunes Music Library.xml" from the iTunes folder under My Documents from my PC at home (where I do all my music management) and overwrote the same two files on my Mac at work.
Now I can plug my iPhone into my work computer and have full access to it. No more music grayed out!
I think I'm the last person to figure this out. Decided to post about it, in case there are others. :P