I mean…probably because it's a tv show so they put something on the chalkboard for visual purposes and the building is 200 years old. But the EW article makes it very clear she's a journalist. Plus, Paris is at Chilton as well and they only filmed their for a day, two at most.

What do we have to do to make that crossover happen? Kickstarter?

Eventually, other people will read the EW article and learn that Rory is not a teacher. She's a journalist. She's just visiting Chilton.