Did they even have a fence around the WH back then?
I don't think so. One famous story from that era was of a guy driving down Pennsylvania Avenue in a convertible, when a rain storm broke out. He pulled in under the awning of the White House to pull up the top, and a White House Usher came out and helped him.
No wonder punks like Ezra Klein don't have a clue what a constitutional republic look likes. If you tried that today, you'd be blown up by an anti-tank mine before you even hit the concrete barricades.
Looks like a fence to me in the full size picture.