I'm not confused about anything, Tether.
Nor do I have 'lowest common denominator' bleeding heart liberal thinking.
Sickly kids, up to a point, have to recognise their condition. I see no point in penalising healthy kids.
The attendance problem in lots of schools is often down to over-protective parents who let their children stay off school for the tiniest niggle, or let them take a whole day off when they are having their braces tightened, or the day off after a DofE expedition. Perhaps they get the day off because their younger sibling is in a nativity play or their elder sibling has given birth. Sometimes mum is just lonely and she wants to keep her lovely DD at home. There are lots of non-medical reasons for absence - social reasons affecting all classes. And yes, it is the parents you need to get through to but there is the well known notion of 'pester power'.
The bottom line is that a student needs to be in school when their health permits. If a school has found a strategy that works, then good for them.
If you adopt a 6 sessions of counting attendance strategy, it will really only be the chronically ill who will not receive an award (but perhaps they could get a different one, for overcoming difficulties). The chickenpox, flu, D&V will just affect one attendance period.
I can't think of any days off my children have had in the last 5+ years. They don't get to take days off unless they are unable to keep their fluids where they belong.