The odd situation came in Kuchar's 2-up victory over Spain's Garcia in a quarter-final match at Austin (Texas) Country Club.
Garcia missed a seven-foot par putt at the par-3 seventh hole, his ball an inch from the cup, set for Kuchar to concede and halve the hole.
But an irked Garcia followed his shot by quickly brushing the ball and it lipped out, all of it before Kuchar could concede the putt and as a result, Garcia lost the hole.
That led to tense moments for the remainder of the match, notably an exchange between the two on the 10th hole which Kuchar later said was the two getting "on the same page."
"I said, 'Sergio, I didn't say anything. I'm not sure how this works out,'" Kuchar said. "I didn't want that to be an issue... Sergio said totally his mistake. He knew he made a mistake."
But when Kuchar added, "I didn't want that to be how a hole was won or lost," Garcia replied, "Well, you can concede a hole."
"I thought about it and said I don't like that idea, either," Kuchar said.
Garcia, who was disqualified from the Saudi Arabia International in February after damaging several greens in frustration, admitted his blunder after the match, which he took to the 18th hole before being eliminated.
"I screwed it up. It's as simple as that," Garcia said. "I missed my putt and I kind of tapped it with the back of my putter before he said anything.
"It's a loss of hole. I understand that. The only issue was that Kooch was like, 'I don't want to take the hole. I don't want to do this like this.'
"So I was like, 'OK, it's fine. What do you want to do? Because there are many options that you can do if you don't want to take the hole, even though I've already lost that hole.'
"But obviously he didn't like any of the options that were there," Garcia said. "It's fine. At the end of the day, I'm the one that made the mistake."