Why Was This Ball Called Fair in New York?

After HP Umpire Lance Barrett signaled fair when Yankees third baseman DJ LeMahieu swiped his glove at Royals batter Bobby Witt Jr's bunt, New York seemed perplexed by the lack of a foul ball call. 

To solve this riddle, we must first consult the rulebook definition for "Fair Ball"—

"A FAIR BALL is a batted ball that settles on fair ground between home and first base, or between home and third base, or that is on or over fair territory when bounding to the outfield past first or third base, or that touches first, second or third base, or that first falls on fair territory on or beyond first base or third base, or that, while on or over fair territory touches the person of an umpire or player, or that, while over fair territory, passes out of the playing field in flight."

Within this wordy definition appear two criteria for determining whether a ball is fair or foul: in some cases, the ball must be on fair territory/ground in order to be considered fair whereas, in others, the ball may be either on or over fair territory/ground.

For example, a fly ball to left field must first fall on fair territory. But notice that for the Royals-Yankees play—fielder LeMahieu physically touching the ball prior to first or third base—the ball may be either on or over fair territory when touched in order to be deemed fair.

Thus, even though the ball itself was in contact (or on) with foul territory, part of the baseball's sphere was positioned over fair territory when first touched by LeMahieu, and, thus, the ball was ruled fair.

Video as follows:

Alternate Link: Umpire calls bunted ball fair even though it didn't touch the foul line...why?