Interestingly, interruptive presidential security is a relatively recent development. Truman used to walk freely around Washington, DC and his security staff didn't do much to stop him.

During the assassination attempt at Blair House, Truman actually opened the second story window and peered out to see what all the gunfire downstairs was about. (If I remember my McCullough correctly, he walked back to the White House just a few hours later with essentially no security.)