What is it here you need to know? This story seems a bit confusing. About all I can say is what I have researched in the past and know. The KHJ calls were assigned by the Department of Commerce on March 13, 1922. But, I'm not sure if the 3-letter calls were always assigned in sequential order, because broadcast stations KHQ in Spokane and a license for KGF-Pomona, which was never built and never went on the air, were assigned in February 1922, before KHJ. Other 3 letter calls were issued for radios on ships and land code stations, such as KHI for the Southern California Edison company. I haven't found out yet what the KHG and KHH calls were assigned for.
So, while the 4 letter calls for radio stations, which came about in mid-1922, were assigned in sequential order, this was not extactly the case for 3 letter call signs.
Their statement is basically true about the slogan "Kindness, Happiness and Joy." The C. R. Kierulff electronics company, which built KHJ for the Los Angeles Times, did not request the call letters. Near the end of March, when the newspaper printed a story, about their new radio station, with the calls KHJ, they suggested that the call letters "might stand for Knowledge, Happiness and Judgement." (C.R. Kierulff sold the station to the L.A. Times in October of 1922.)
The Times Radiophone station, KHJ, finally went on the air officially on April 13, 1922. Soon after that first broadcast, John S. Daggett, the station's manager and announcer (also known as Uncle John), came up with the slogan "Kindness, Happiness and Joy", and it stuck for several years, at least until the L.A. Times ownership of KHJ ended in November of 1927. Uncle John Daggett was KHJ's announcer and station manager until the station was sold to Don Lee, in late-1927.