Before There Was Walmart
There was Kenmore.
Sears does not merely slap their brand name on whatever a manufacturer is churning out, rather it insists on certain design and other changes for it's models. Furthermore the appliances are not produced as part of the main run, rather the plant in question shuts down other production, and or makes arrangements so only Kenmore's are produced for that period.
Unless things have changed, Sears used it's position as the number one seller of major home appliances not only to insist on changes, but pricing as well.
With the above in mind it is not hard to see why there could be differences in reliablity between a Kenmore appliance and it's branded cousin.
Case in point; my "Kenmore" branded 18" dishwasher is made by Frigidare/WCI (or whatever it is calling itself these days). Read all the reviews at the time for the later but went with the Kenmore mainly because could use my Sears card and save some money. While the Frigidaire had horrible marks including for reliability, so far after >ten years other than one door spring going, my Kenmore has had zero issues.
Of course with the race to the bottom we are seeing with major appliances, Sears/Kenmore has not been immune. However am willing to bet much of this can be traced back to Sears not being top dog anymore in appliance sales, and indeed the company's fiscal woes all together leading up to being purchased by K-Mart.
There was also a time when Sears in-house service techs took care of anything one purchased. Now for the most part I've heard the work is contracted out and the word on the street here and on the Internet is to run fast, run far.