No, it's not.
Medical professionals gauge whether or not a person is breathing, specifically, by determining if they can speak or not. If they can't speak, they know they are out of time. if they're talking, they know they're breathing.
Try talking to an asthmatic on the topic.
Yes, they can technically "breathe," but that doesn't mean that their pulse-ox isn't dipping dangerously low. If you're not getting a good amount of oxygen, then you feel it.
Eric Garner was clearly breathing. But it might have taken a lot more of his time and precious oxygen to try to stammer out, "I am not getting enough oxygen with each breath, and I feel like I'm suffocating."