Shared housing is fine for those who will accept it and clearly know that they're getting it. My problem here is simply in not being clear that you're getting shared housing...
Of course I don't know the particulars on how they do housing. They may be happy to help you find something, but they won't pay for more than 1200 a month towards it.
But they don't tell you something else...if you rent the apartment on your own, you'll have to cough up a deposit and most likely at least 3 months' rent and God knows what kind of agent fee, just to move in. They're giving the choice of paying up a big wad of money up front, or taking shared school housing.

Chongqing isn't terribly rich, at least not compared to the towns on the other end of the river. 1200 per seems awfully low but I don't know current market prices there...