Should high schools bar average students from rigorous college level courses and tests?

Jay Mathews has a column about this in the Washington Post this week.
I know it's an issue that has come up in a number of districts I've covered over the years. When I was in Maryland, the district I covered opened Advanced Placement courses to everyone. The thought was it would be good exposure for students to be in rigorous courses. Even if they didn't get the best grades in other classes, it would help expand their thinking and prepare them for education after high school.
When I was in Altoona, the district had specific requirements for students who wanted to take AP classes. They weren't open to everyone.
How does your district handle AP and IB courses? How do you think they should handle them?