You made my point because you admitted that the metric was, in fact, measuring the value of a player's contribution relative to a replacement player at his own position. If that weren't at least a partial aspect of the stat, there'd be no reason for the positional adjustment. You'd simply compare players to the total contribution of runs created/saved. You don't need to know what position someone plays to compare what they produced. We already know that without finding the replacement level of the position. You can already compare Mike Trout to Ryan Braun to see who the *better* player is. You need the positional adjustments to see what *value* they have over a replacement at the position they play.
We can argue semantics all day, but the bottom line is that the stat does absolutely measure replacement level over same position players. That's exactly what the output measures... the number of wins above a replacement player at the same position. It's astounding to me that anyone is disagreeing with that simple statement. That's the whole calculation in a nutshell. We can argue semantics at the 'purpose,' but that is in fact what the stat does.
This is basic economics. Some products might not have as good of quality as another product. But supply and demand might make that product more valuable despite being of a lesser quality. WAR doesn't aim to measure the quality of the product, but rather add in the supply/demand value aspect of the positions.
One last time... Ryan Hanigan isn't a better baseball player because he plays at a position with lesser talent. All that means is he's a more valuable baseball player. WAR is meant to measure value, not necessarily talent/production. You don't need to know replacement level to compare players across different positions if all you want to know is who the better baseball player is.