Okay, I may be only 50, but my childhood memories of the Berlin Wall always involved someone being shot for going to close.
I can hear the East German guard now "Don't shoot! That is the cute little boy who will one day grow up to be President because he was born in the West Wing! He will be our friend."
You are partially correct.
Once you crossed into East Berlin through the checkpoint you saw a flat area behind the wallthat containe mines. It wa about 30-40 yards wide. The also had barbed wir below and on top of the wall. Guard Towers every 100 yards.
If an East German tried to cross over, he/she was probably shot.
Through the checkpoint though, no big deal. If you had an i.d. card and drove through, you couldn't roll down the window, you had to show your ID to a "Russian" guard. Civilians were examined by East German guards.
There is a very interesting Museum at checkpoint Charly. Amazing stuff.