Would you be offended if it was a black person who came in saying all white people smelled?
Personally, no. Just like with the old lady, I would just think it's a little ignorant.
However, there is a huge difference between having a private discussion with a friend and a person spouting off in an obviously negative manner in a public place to the point of having other people look at her like, "What the fuck are you talking about?" I couldn't even begin to imagine the chaos that would ensue if a black person came into my work and starting going off in a very public and negative manner about anything about white people.
EDIT: I didn't see that you said, "came in," as in came into my work. Yes, I would feel the exact same way. In fact, the lady was getting to the point that we were going to have to tell her stop because she was violating building policy. I would do the exact same thing with a black person. Though, like I said, the little old white lady got away with it, whereas I doubt a black guy would get away with it in the same manner.