You know what IRstuff, I thought the same thing when I started reading the sites and they said about knights jousting but I didn’t want to take this even more off topic. I've been to a couple of re-enactments and they always rode on the right, keeping their shields to each other.
However, I believe knights/soldiers usually only carried their shield when dressed for battle but the sword itself was often carried as part of everyday dress. Also shields went out of vogue some time before swords went out of style, just think 3 Musketeers etc.
So it’s probably not unreasonable to assume that for much of the time throughout history people did only have the sword and hence having your sword hand toward any potential threat was a sensible precaution.