At my daughters' school, it is very similar. After 5 sick absences, you need a doctor's note for it to be excused. If you pick them up after a certain time during the day it isn't an absence. I had to pick up my oldest because she had a migraine. I got her at 11:00. I think it was an absence.
I don't know why they are cracking down so hard. I guess for the parents that let their kids stay home for nothing, or don't know the kids are not there.
momz