Quote from your linked article: "The Book says the #3 hitter comes to the plate with, on average, fewer runners on base than the #4 or #5 hitters.''
...
The number four position has the most over the course of a season. In fact, it's 104 times more than the leadoff position, quite a significant difference. The third spot in the order is not far behind.''
Two articles, one says #5 bats with more runners on base, the other says #3 bats with more runners on base.
Somebody's stats are lying.
Let me help with that:
1st, the Bill James Onine article only uses 2006 data, it fails to consider the number of runners on and the number of outs, and it disregards the total number of PA. The list you used ignores the number of PA completely, so shouldn't be used for a comparison. The data needs to be normalized:
You can see that the difference between 3 and 5 for 2006 is even smaller than it looked initially.
Contrast that with the data used in The Book, which is drawn from decades of baseball data:
So, the #5 batter sees more runners on per PA, sees 0 outs far more often, and sees 2 outs far less often.
It's never as simple as a single number.