It looks like that site, www.whitehousemuseum.org is down for the time being. Google still had a smaller version of the picture, so I copied it to the Zone's gallery here:
I believe that we have established that the picture is of the White House c. 1870 and that "what happened" occurred between the end of the Civil war and the building of the wings.
wagga made a post about the sesquicentennial of the Civil War and this was the sesquicentennial puzzle -- seemed relevant at the time, but the Civil War did not end in the White House.
