Pensions for teachers are certainly common. I grew up in a completely different part of the country and all my teachers also had pensions. I'm not sure how the median income is a poor indicator -- she makes as much as the median household does for the city.
For a long time there was a bizarre loophole in Texas. Apparently, the decision whether or not to pay into Social Security was made on a per-school-district level. Most districts do not, so do not receive Social Security. Some do, and those retiring from there did get SS. The super-secret trick was to resign from your current position, somehow work for a week or so at one of the minority of districts, then officially retire and collect both your normal pension and social security. I have no idea how it actually worked, I just watched a couple of teachers of my acquaintance do it.
I believe the loophole has been shut down for several years.