Courtesy of Wikipedia
... However, the scabbard tended to slide around a lot when they charged the enemy, meaning that it had to be steadied with the left hand before being drawn.[4] ...
I confess to being a total nerd and once being heavily into Medieval sword fighting (not re-enactment but the martial art ( for example, this group run by a mate of mine in Germany
http://artsofmars.com/ ) - I was into an Italian longsword style myself ...). In fact, all types of sword in any scabbard need to be drawn with the left hand on the upper scabbard assuming you are right-handed and not wearing one of those silly back scabbards common in films (movies) in which case you would have a difficult job staying alive unless you drew the sword before starting your charge.
I think that the Sam Brownie belt was probably invented to stop the sword banging about as you ran with a pistol or rifle. A sword only becomes a weapon at distances of about one metre or so.
Perhaps an ex-forces person could comment?