I think that this has been discussed here before, but I was watching a little NIT tonight -- kind of warming up my watching skills for the Big Dance, and I heard this ridiculous expression. The announcer said that Vanderbilt had a lot of guys who knew how to "score the ball." This is right up there, IMHO, with "score the rock." Can't you just say, "lots of guys who can score"? Or, lots of good scorers? I wonder what things will be like tomorrow weather-wise? ;-)
There was some comedian who brought this up for some reason a few years back. I just remember the follow-up being "what else are they supposed to do with the ball, punt it?"
The difference is that punting is actually something done TO a ball. points are scored. runs are scored. balls are thrown, hit, passed, fielded, kicked, caught, punted, dropped. The only time they are scored is at a Ginsu demonstration...and that would be an odd ginsu demonstration.