That's not quite what it says. True, a run is a run is a run on the scoreboard -- but over the long run, it's worth more to a *team* to score or prevent runs at positions where the talent to do so is more scarce. That is what WAR is estimating, to complement what we know from the daily scoreboard.
The defensive spectrum has been known in some form or other since the game began. The skill of playing as an average defensive CF, SS, or especially catcher is much more rare than the skill of playing as an average defensive 1B (or god forbid, DH!). And with that rarer defensive skill, it also means that, on average, it is slightly harder to find an average MLB bat at those positions too. Historical data bears this out.
So a team isn't capturing as much value from Ernie Banks at 1B as compared to SS, or Joe Mauer at 1B compared to C. WAR is reflecting that. And baseball teams are bunched close enough together in talent that I guarantee front offices wouldn't shrug it off as "a run is a run is a run" if they can help it -- they are going to want to reallocate those resources to improve their team relative to their competition.
WAR isn't necessarily an absolute measure of a player's performance. It often can be used that way, because teams generally don't play guys out of position too much or for too long -- but it's important to keep in mind that it is really a measure of a player's value within a team, or their value as deployed by a team. I'll gladly include an asterisk if I have reason to discuss Darin Erstad's WAR at 1B, but that doesn't mean WAR is good for absolutely nothing (say it again).
This. but it's also noting that the defensive impact on run prevention at some positions is larger than others through sheer opportunity as well. there are simply fewer opportunities to make run-saving defensive plays at 1B than at CF. WAR is a useful way of summarizing a players total contributions to the team in a way that's fairly easy to understand, and in doing so it recognizes that certain positions are more valuable than others. That's all the positional adjustment really does.
(it's also important to note that fWAR and bWAR are very different estimators for pitching; fWAR tells you how good they think a pitcher should have been, attempting to null out luck factors. bWAR tells you what they actually accomplished for the team in that year. fWAR may be better for predicting future success. bWAR is more descriptive of what actually occurred.)
It's a useful tool, and it's nice to have a stat that tries to bring in everything about a player. It's not the end all be all, but it's a useful starting point for any discussion about a player's value. To my mind, if you have to argue that a player's WAR doesn't mean anything, then you have a weak argument.