I saw the video a couple days ago, and my first thought wasn't that the coach was arguing about the tag - I thought he was arguing about the baseline.
I don't know what the college rules are, the MLB rules say:
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7.08
Any runner is out when --
(a) (1) He runs more than three feet away from his baseline to avoid being tagged unless his action is to avoid interference with a fielder fielding a batted ball. A runner’s baseline is established when the tag attempt occurs and is a straight line from the runner to the base he is attempting to reach safely;
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I think the coach was arguing that the runner was out of the baseline, vertically.
But I really think he was trying to avoid embarrassment.
I think he was safe, but it just doesn't feel right.