Should we be using profiles or just the driver when printing B&W?
What does the printer do, does it print with black, grey and the light colours when it does a B&W?
For non-toned BW the HP recommended workflow is for application management, ie "Let PS determine colors". If you are going to enable any gray balance corrections the recommendation is for printer management, ie "Let Printer determine colors", in which case the printer profile menu is unavailable in PS. In either case make sure that the document's source profile is correct.
If you send a grayscale file to matte paper the Z3100 uses MK, PK, G, LG, no color pigments. If you send a grayscale file to glossy paper the printer uses PK, G, LG, GE, again no color pigments used. If you send an RGB file, any pixels with equal RGB values get printed with either the tri K or quad K setup mentioned above, depending on matte or glossy media. Obviously if you enable the gray balance settings, color pigments are used to hit the requested tint.