I was recently at a Toyota dealer getting my dingy (2010 Toyota Yaris) serviced (regular maintenance). I was walking through the showroom looking at the vehicles when I was approached by a salesman. He asked about my current car and he decided it was time for me to "upgrade"-. When I told him how we use the vehicle being towed four-wheels down, his attitude deflated and he told me that NONE of the new Toyotas can be towed 4 down. He then walked away.
I would definitely check and make sure that the Corolla can be towed all wheels down.