What I didn't mention were the teams that started the season on a losing streak. And now, heading into this weekend's play, the 0-6 Red Sox and Rays that are getting the attention of the punditocracy. For the Red Sox, it's the poorest start since the 1945 season, and the Rays haven't ever gone 0-6 to start the season in their comparatively short history.
Some writers have acknowledged the probability and the history of being 0-6: Dave Cameron at FanGraphs writes "Is it time to panic in Boston?", and Cliff Corcoran at S.I.'s piece is "It's still early, but history is against winless Red Sox, Rays and Astros" (which was written before yesterday's games, when the teams were 0-5).
An entirely different view can be found Baseball Prospectus, where Steven Goldman uses the 1987 Brewers, who went 13-0 and then 20-3 (Goldman writes, "on pace for a 141 win season") before hitting a 12 game losing streak, and the opening sequence of Tom Stoppard's existentialist play Rosencrantz And Guildenstern Are Dead to suggest that sometimes things operate outside the laws of probability.
(Watch the scene in question, from the 1990 film with Gary Oldman and Tim Roth as the title characters.)
In the play, the characters are faced with a preposterously long string of coin-flips that land heads. This leads Guildenstern to say "A weaker man might be moved to re-examine his faith, if in nothing else at least in the law of probability."
Even though the two teams are 0-6, the weakness of my faith in the laws of probability is not yet tested.