He is right though. My dad teaches UFC and other martial art sparring stuff. You NEVER use your fist for those reasons.
As for blocking your elbow is great. If you are able to put some of your hip (just for extra power) and they throw a punch... if it hits your elbow (one of the hardest bones in your body) they can shatter their fist. The face isn't the first thing I would aim for either. There's a series of moves ( I'll try and find a video) where you hook your hand at the back of their neck. Main reason is once it's hooked you can do what you want with them. You move your hand in any direction their body will follow sine it's such a strong pressure point.