The reason why the proposal is made in public when they have no clue if the person wanted marriage is to force the one who receives the proposal into a situation that makes them look bad if they reject the proposal. It is a manipulation tactic.
The truth is that the discussion about marriage should have already happened multiple times, and the person preparing to propose should already know that the answer will be yes before the public proposal is made. The public proposal is just suppose to be an open declaration of their love and move towards marriage for everyone else who does not know, it is not suppose to be the time you find out if marriage is on the table or not. That question should already be answered before the public is brought into it.
So no, rejecting a proposal in public when it was not agreed to already in private is not some low emotional EQ act or the person being devoid of empathy. It is instead not allowing the person to emotionally blackmail you into accepting something, in this case marriage, you never agreed to in the first place. Like I said before, it is a manipulation tactic, hoping you will not allow them to look bad in public and so in turn hoping to force you into accepting something you never stated you wanted.
Just because a woman made the proposal does not change anything I wrote above.