Hmm. This seems like a topic that could open a can of worms around here... People have strong opinions!
My mom had the unless-you're-sick-or-dying mentality, and I, like your son, was the honor roll, AP classes, part time job kind of good kid. I wished my mom would have had just a bit more flexibility to her - letting a kid miss a day of school as a mental health day, for a single day, is not going to suddenly cancel out the honor roll, the good grades, the job... all that good-kid stuff will still be there the next morning. (Though I'd wholeheartedly agree that you don't get to skip the day there's something particularly important going on - a major exam or project due date, for example.) Basically, in schools today, there's a lot of pressure on kids (and 16-almost-17 is still just a kid!) to keep up, work hard, test well, etc. It's absolutely good practice for adulthood, when we do have to step up and be adults... but they aren't adults quite yet. To my mind, letting a kid take a day off from the daily grind won't hurt him.
So I said I'd parent with a little more flexibility, and so far, I have. But, full disclosure, my son is 6, not 16. So I'm not dealing with high school and teenage attitudes yet!