I spoke to the U.S. LAN reservations line 866-IFLYLAN and they confirmed that I am entitled to the fare difference and a free business class ticket.
I still think it is too generous (not that I'm complaining), but I guess the cash difference isn't really compensation, but money to which I am legally entitled. The free J class ticket is the compensation and very generous at that.
I am not sure that getting it issued will be easy, but I may be wrong.
LAN is definately a class act and, I as I have said before, the second best carrier in Oneworld.