Sears did design/spec the Dual Action agitator. Whirlpool built millions of belt-drive washers for Sears on a "gentlemen's" agreement, meaning no actual contractual committment was signed for years between Sears and WP regarding how many machines Sears was committed to buy, etc. Sears simply placed purchase orders for various models whenever they wanted to. This has since changed....
Sears spec'd the DA, the Vari-Flex, the triple dispenser, and other Sears-only parts. WP's position was that if they can make it, and profitably, they'll do it. So, Sears said "here is a design, make it happen" essentially, and WP did. Such was the case with the DA agitator, with which Sears enjoyed a 15-year monopoly. I don't know what wranglings happened after that, but WP came out with a similarly functioning auger agitator in the early 90s (it used the same base in fact), and it was then a WP/Kenmore exclusive. When the patent finally expired, the rest of the market quickly copied something similar.
As far as the Kenmore only Direct Drive, I disagree. The first models were issued by Kenmore in 1981 and 1982, in very limited form (24-inch standard capacity, and only a couple models) and Whirlpool did the same. The direct drive machine was Whirlpool's concoction with Kenmore's acceptance, and was done as a reaction to the rising manufacturing cost of the BD, which was going up faster than sales prices.
There may have been a focus on Sears with the first direct drives, but this was probably due to Sears' market penetration, which would put more "guinea pigs" out there faster than if WP tried to sell their own only. Those first couple years of manufacturing and sales caused some re-design work and if what I was told is true, some expensive recalls.