Yes they do need to add, and if their math is wrong, they get DQ'd. There's 18 numbers on that card that need tallied, which doesn't sound like a big deal, and 99 percent of the time will be tallied correctly. But only in golf, if in that one percent where they are tallied incorrectly does the player get credited with the erroneous score (if it's higher) or DQ's (if it's lower).
Re comparing basketball to golf, don't miss my point. All I'm saying is, in other sports the players aren't obligated and required to keep the score, and further, if should the player come up with a different number than reality, that number doesn't become fact.
The 18 holes do NOT need to be tallied up for a correct total score for the round. I think that's turtleback's point, and one which a lot of people are unaware. The players ONLY responsibility is to mark the correct score for each individual hole, not for ensuring that the total score for the round is correct.