Yeah. But as others have noted, the fundamental problem here is that the runner is required to run to the first-base bag, and the bag is not in the running lane. At some point, the runner must exit the running lane, if the runner is to run to/through the bag - which is required. As long as the runner is required to run outside the line, and the runner is required to run to the bag, and the bag is inside the line, there are going to be occasions where the necessity to go to the bag results in potential interference calls. Because of this inherent conflict, the umpires must make judgment calls - not subject to review, because review would just be substituting the judgment of an umpire in NYC for an umpire on the field.
Looking repeatedly at the replays... Turner was never in foul territory (not uncommon with RH batters, who begin their run far to the "fair" side of the first base line). Given that, it's not unreasonable to conclude that, had he been outside the foul line at any point, his angle of approach to the bag would not have resulted in a collision with the first baseman's mitt. So the interference call is defensible judgment.
Couple of further observations:
Fortunately, this call did not affect the outcome of the contest. It may have cost the Nationals a run... but they won the game.
It's kind of a shame that the real mis-execution on the play - the pitcher's crappy, off-line throw that resulted in the 1B's attempt to catch the throw well in front of the bag - and in the lane of approach to the bag - doesn't get reflected in any way in the scoring. Better throw, and the runner would have been out, no argument, no nothing.