I'm no expert either, but as far as I know, analog equalizers always cause phase shift. That is one reason why audiophiles don't like equalizers.
What the writer of that paper is saying, is that not only frequency response changes, but also phase shifts occur in a room. Hence, you need not only to fix the frequency response, but the phase shifts as well. That's why, he argues, it's a good thing that equalizers cause phase shifts.
I'm not sure whether that's a valid point. It seems to me that phase shifts caused by the EQ are in a fixed relationship with the amount of boosting/cutting. When you need to compensate for room acoustics, you can't know whether that predefined relationship suits your room.
But don't take my word on it, because I'm not expert as I said.
Here's a link by the way to a manufacturer who makes digitally compensating equipment:
Lyngdorf.