Well that sucks! Did you tell them that other Corolla owners have been having the same issue?
I honestly have no idea what the difference between the parts are, you know more than I do about the parts and pricings. Did you go to
www.toyota-parts.com? I did a parts number search to see what it is and they have it listed for $118. You could go to a junkyard and see if they have a 2010 Corolla there with that part, I'm sure you could get it for half that price, then go to a local mechanic shop and have them install it.
I'd search on the Car Talk mechanics files for recommended locations, especially if you don't want to pay an arm and a leg and sign over your first born child to the dealership for repairs.