Interesting that they bring that up. People in general have a very poor understanding of statistics and probability, and they're both rather germane to discussions of baseball. While the result the articles are discussing is pretty basic (basically they're explaining that players (or coins or whatever) are never "due" to have a particular result because they haven't had that result in a while), it leads naturally into the discussion about projecting players and just how strong the correlation between your previous AB and your next AB is. (My guess is that it tends toward zero.) But in a sense, this is the crux of roster construction in fantasy baseball (and real baseball, I suppose): which factors are most important in predicting how a player will perform this season? Next season? The second half of the year? For some player, like Mark Teixeira for example, there is a definitive trend of slow starts and late surges. So while Tex has been sub-par thus far, it's reasonable to expect him to out-perform his career norms the rest of the year and finish around his usual spot. While the conclusion is similar to that we'd get from using the "Gambler's Fallacy", the reasoning is different and, in this case, correct: based on data from previous years, Teixeira is a player who tends to perform better as the year goes on. With other players, such as Travis Hafner, we may not suspect a turnaround given the similarities between his career and those of other high-peak, quick-flameout guys. (This is essentially what PECOTA does.)
All this is just to say that when we try to predict how players will do in the future, it is important for us to note what factors we're looking at when making these predictions, and most of the time, year-to-date numbers don't tell the whole story.
"I don't buy everything I read,
I havn't even read everything I've bought"
"I find it more comforting to believe that this [life] isn't simply a test."