Please explain how you open a pull door with your back.
In any case, I still think there is risk having this ambiguous button like thing, both from passersby bumping it and from normal use. And, as my comment (and the immortal Far Side comic) illustrates, many pull doors and push doors look confusingly similar, so people will push the pull handles.
Also, may I suggest making your correction in a friendlier way next time? Especially because it is possible that the person you're correcting may not be the total doofus you imagine them to be!