You asked us to take a look at a Replay Review decision that overturned 1B Umpire Paul Clemons' safe call on a play at first base when Red Sox batter-runner JD Martinez lunged for but missed touching first base as Yankees first baseman Marwin Gonzalez stretched to receive a throw.
Although there exists an MLB Umpire Manual interpretation holding that a runner shall be declared "safe" even if they miss a base based on timing alone, the fact of the matter is that in this case, the batter-runner (by virtue of being short of first base) hadn't yet reached first base when the fielder first possessed the ball. Had batter-runner Martinez instead overstepped first base and failed to touch the backside of the base after already having reached it, then the proper call from Replay would be to declare the runner safe, unless New York were to have filed a proper appeal before manager Aaron Boone challenged the play.
From MLBUM: "If the batter-runner misses first base, or a runner misses their next base, they shall be considered as having reached the next base, as referred to in the Note to Official Baseball Rule 5.06(b)(3)(D) and as stated in the Approved Ruling of Official Baseball Rule 6.02(a): 'A runner who misses the first base to which they are advancing and who is called out on appeal shall be considered as having advanced one base for the purpose of this rule.'"
If the Yankees failed to appeal prior to requesting a Replay Review, it would be too late to appeal after the review's conclusion and the runner Martinez would be ruled safe if the Replay Official determined his foot missed first base, but that the runner did, indeed, reach or arrive at first base prior to the fielder possessing the baseball.
Video as follows:
