I'm not an expert on any type of bird. I'm simply an owner and cannot give you a scientific or proven approach to whether or not African Grey's can actually understand what they are saying.
In my experience with Gracie, I see she mimics a lot of what we say. She understands basic commands and is stubborn from time to time as to whether she'll actually follow the command, i.e. the "step-up" command is followed most of the time except when she's on top of her cage (we try not to let her perch higher than our heads) or if she simply doesn't feel like it. She hasn't (so far since she's not 2 yet) exhibited any intelligence to actually comprehend what she's saying.
I have to say, though, she surprises my husband and I on occasion. Pebble, the Senegal, fell off his perch the other day (he's still getting his sea legs) and Gracie promptly said "Ouch" which is something neither my husband nor I have ever taught her to say.
Gracie's grammar is pretty darn good although most of the time she only lets loose on it when she's in her quiet times in her cage. She'll have her back to us and sit and talk to herself. She can say "What cha doin?" and many other phrases but she won't say these 'on command' if we ask her. She repeats a lot of what she hears on TV even the "bad stuff" as it were. My husband is attempting to get her to whistle tunes like "Everybody was Kung-Fu Fighting". I'm trying to get her to sing "If I only had a brain" (just that one phrase).