Sickness absences count as authorised.
These proposals aren't changing the underlying policy - just ending the postcode lottery of the discrepancies between different councils about when fines are levied.
I'm less sure what the intentions are about monitoring high levels of sickness absence. If a child is missing a lot of school, then finding out why and seeing if the family needs extra support would seem sensible, but i can quite see why people would be mistrustful on that.
I expect it's a response to parents who lie about sickness as the reason for absence. This has already led to some schools asking for evidence of the medical need. That's another hoop for parents of DC with chronic health conditions to jump through. But don't kid yourself that it's not already happening in some places