The story starts out with the lie that teachers get paid for 12 months work & only work 9, most just choose to spread out their 9 month pay over 12 months. As far as insurance goes, if any districts provide free insurance I've never heard of them, to cover yourself and your spouse the monthly cost is over $1,000 in our local district.
I never understood the teacher hatred some people have, if the author really believes what he writes, maybe he should try being for a teacher for a while.
Where I am there is 10 months of work, 2 off for summer. You get to choose. If you want (and are nuts) you can get paid only for 10 months, or as you said, choose to spread it.