Only at the beginning of the season would a four-game winning streak get you an article on S.I.
The probability of a true .500 team playing four games against other true .500 teams and winning them all is 6.25% -- or roughly 2 out of 30. In other words, at this point in the season we could realistically expect two teams to be at 4-0. Once we consider that in real life teams are not so perfectly matched, thus raising the odds of the more powerful team being successful in all four games, the fact that there are three teams with 4-0 records (Orioles, Reds, and Rangers) isn't a surprise.
The only surprise in all of this is that the Orioles (widely touted to finish last in the A.L. East) swept the Rays in a three game series in Tampa Bay and then went on to beat the Tigers at home in their fourth game of the season. But then again, the probability of a .400 team going 4-0 against a .500* team is just under 3%. Not very good odds, but something we would expect to see on occasion.
(Shout out to Tango, who raised the "on pace" problem a couple of days ago, and The Book readers who added various lucid and perceptive comments, including an XKCD cartoon. You can never go wrong using an XKCD cartoon to illustrate your point.)
Update: the New Utosky Bolshevik Show takes the Red Sox 0-3 start as its jumping off point for a post titled The Red Sox Aren't Doomed, demonstrating the same thing I did but with graphs and Python script. Score one for the NUBS.
* Changed from ".600". Comment #1 below was generated because of this typo; #2 is my detailed response.