I've heard several people say something to this effect lately. Apparently, the all-or-nothing attitude towards specific exercises is pretty pervasive out there. Frankly, I don't understand or agree with it. Granted I can get pretty dogmatic about training but I just don't see the point in being that strict about an exercise.
If someone can only do half of a push-up, isn't that better than no push-up at all? When you're just getting started, anything is better than nothing and if you're weak, then you can build strength doing half push-ups. Don't get stuck on what can't do; focus on what you can do. Then, work from there.
Besides, there comes times in life where you may be physically limited to doing less that what you're accustomed to. I recall a few years ago that I fell and hit my elbow hard on the way down, swelling my right elbow up grotesquely. I found out that while I couldn't go full-range on normal push-ups, I could go wide-handed and get almost all of the way down on that push-up. It may not be the most intense push-up that I ever did but it still kept me in good shape. It was sure as hell better than no push-ups.
There is no lawbook to exercise that tells you that you can't modify an exercise to suit your physical needs. Don't ever feel like you can't tailor and trim according to your body's needs.