That's a fairly whitewashed description.
The officer was about 6 feet from the lady as she climbed through the window. Her body was almost in full view. It should have become apparent that she wasn't armed. There were people standing in the same protected hallway who didn't appear as though they thought there was an immediate threat.
There were also police on the protestors side of the door who also didn't appear to think that there was an immediate threat.
Add to that there doesn't appear to have been any other cop anywhere in or around the Capitol who thought they needed to shoot somebody.
All that aside, you don't break into buildings especially ones where you know there are going to be armed LE guarding high government officials.
He broke cover to move closer to her to get a better shot. Murder.