Cliff Corcoran at SI.com noted that while roughly the same amount of teams started a season 0-5 (110) as 5-0 (105), starting the season hot seems to have no strong bearing on a team's ability to make the postseason yet starting a season cold does. He theorizes that the timing is the culprit.
It's simpler than that. It's because there are so few postseason spots. Only 25% (8 of 32) of the teams make the playoffs - and that's now. Before the Wild Card kicked in the numbers were lower - in 1968 you had a 10% chance of making the playoffs, in 1994 it was 1 in 7.
If half the teams made the postseason, like in hockey or basketball you'd expect these starts to be roughly as indicative of making the playoffs. But because the majority of baseball teams go home, it's tough to turn a 5-0 start into a playoff run and even harder still to turn an 0-5 beginning into one. This makes a bad start a killer, but a good start not necessarily a... life bringer?
Think of it this way : An 0-5 start means it's slightly more likely you are a bad team. Bad teams don't make the playoffs. A 5-0 start means it's slightly more likely you are a good team. Good teams make the playoffs sometimes. Corcoran says something like this about the bad teams, calling an 0-5 start "revealing", but it's the fact good teams don't make the playoffs at the same rate that bad teams miss 'em that drives the difference in usefulness in predictability.
The good news for the Sox is that it's easier since 1995 than it has been to come back from an 0-5 start.