You should care because it reveals the truth about statistics. If you choose the right metrics, you can suit pretty much any agenda. You said that stats exist to reveal truths, but stats can be used to show the exact opposite.
This doesn't mean that statistics are useless, but rather that it's important to question the methodology. In the case of strength of schedule, we can take it to the extreme by compiling a chart after week 1 of the season. All teams that are 1-0 will have had an easy schedule and be ranked in the bottom half because they played against teams that haven't won a single game. Now suppose the Buccaneers played against the Super Bowl winner Patriots in week 1 and won. The strength of schedule chart will show that the Bucs had an easy schedule, but if you actually look at who they played against, then you would know that they faced a top shelf opponent.
The big flaw of the strength of schedule rankings is that teams who win a lot make in turn their opponents worse, because they add a loss to their respective records. On the other hand, teams who lose a lot add a win to the respective records of their opponents, making those other teams appear stronger. When you look at the chart you posted, only two of the teams with a positive record after week 6 are ranked in the top half while the other eight teams with a positive record find themselves in the bottom half. But that isn't surprising, because the teams who win a lot of games have an easier schedule by virtue of winning a lot of games.
Or let's take some other stats that are present in this thread. By looking at your record and win percentage (.110) in the prediction league, we can conclude that you really suck at picking games. But the obvious caveat is that you have abstained in most weeks, so the vast majority of your losses are not due to incompetence. Well, actually you were incompetent by not making picks in the first place. But anyway, the point is that while my chart accurately reflects your achievements in the 2015 season, it isn't truly representative of your ability to make correct picks for NFL games. Therefore statistics can be very misleading, hence why they can be considered worse than lies or even damned lies. They present data that is true at face value, but the metrics used can be chosen and bent to suit the result someone wants to arrive at.