It is evident how the basic definition (quoted below) gives rise to the defintion as "thin concealment", but unclear how it gives rise to the sports usage.
I always thought it was in reference to the blank space on the scoreboard for the whitewashed team. I know that there would probably be a "0" there, but maybe in the good old days the scores would get painted on in a "tally" format (four vertical lines with the fifth a slash through them all to form groups of five) and then painted over after the game. If that were the case, a shutout might look like one team's space on the board had been whitewashed.
I have no proof of the above, it is merely theory, possibly sparked by subliminally remembered bits from Looney Tunes/Merrie Melodies/other old cartoons?
[uncultured aside]When my mother used to listen to "classical" music on the radio my stepfather, brother, and I used to attempt to be the first to identify the Tom & Jerry or Looney Tune cartoon the music was "from."[/uncultured aside]
