Exactly. If a dog views the same scene as me, and it presumably sees only black and white, did we see a different reality? No, we saw different colors.
Off topic, but just so you know -- dogs are colorblind (as compared to us) in that they have a more limited perception of color, but they don't just see black and white (and shades of gray)!
http://www.psychologytoday.com/blog/canine-corner/200810/can...