Did they really? My recollection is that they had a slow and inefficient pipeline that would never be able to handle the speed that Amazon fills order at.

History books claim Sears got slow and inefficient by focusing too much on retail and malls, and shutting down a lot of their classic logistics. In the 1990s they were absolutely slow as a catalog company. In the 1950s, for instance, they were considered fast and reliable. (For several decades the Chicago US Post Office was the largest branch in the country because of it serving Sears' warehouses.)