How many kids ARE in remedial classes?

If you read my notes from over the weekend, you'll know we had a little back-and-forth about college preparation. I keep hearing this statistic that 40% of Massachusetts graduates end up in remedial classes in college, and this is why we need--fill in the blank--the Common Core, PARCC, better teacher evaluation... It hit me over the weekend that we don't have any way of knowing that, as we don't have the data from the kids who go to private school, which, when I asked, Senior Assistant Commissioner Bickerton then added to his citation. (You can find my notes on that here; it's where the all caps are.)
It seems Secretary Duncan got caught in the same trap on his visit to Massachusetts, and Carol Burris pulls out the actual numbers here.
The conclusion (beyond that everyone should check their numbers?):

Using the above, I estimate that the percentage of students in Massachusetts who attend four-year colleges and take remedial courses is roughly 17 percent, not the 40 percent that Duncan claimed.

That's a pretty significant difference, there, people.