Update (January 4, 5pm): Sears has disabled the search feature described above. Attempts to retrieve a purchase history now yield the message "We're sorry, this feature is currently disabled."
There is a further report at ComputerWorld. Although I am not a big fan of Sears, there are many people who still shop Sears for major appliances. It is good to know that their privacy will be respected should they sign up for Sears' "Manage My Home".