in the rule book:

In running the last half of the distance from home base to first base, while the ball is being fielded to first base, he runs outside (to the right of ) the three-foot line, or inside (to the left of ) the foul line, and in the umpire's judgment in so doing interferes with the fielder taking the throw at first base, in which case the ball is dead; except that he may run outside (to the right of ) the three-foot line or inside (to the left of ) the foul line to avoid a fielder attempting to field a batted ball;

In other words, Holbrook believed Turner had stepped outside of his lane on the way to first base and in doing so had obstructed Gurriel from making a play on the ball.

The rule book also offers this additional comment on said rule:

The lines marking the three-foot lane are a part of that lane and a batter-runner is required to have both feet within the three-foot lane or on the lines marking the lane. The batter-runner is permitted to exit the threefoot lane by means of a step, stride, reach or slide in the immediate vicinity of first base for the sole purpose of touching first base.

Predictably, Turner and the Nationals were irate. Turner had to be held back by Asdrubal Cabrera in the dugout, and was seen making references to Joe Torre, who is MLB's chief baseball officer during a lengthy video review. The play was upheld after the aforementioned review, and Washington manager Dave Martinez was ejected for giving Holbrook the what for between innings.

The Nationals then asked to play the rest of the game under protest for a misapplication of the above rule: