Well, it seems to me that if they put the "K" badge on the car next to the name, then that is justification enough to include it in the model name. And just so you know antp, this was done for all years of the model (1981-89) not just some. And just for reference, here is how the badge looked on the car itself:
http://www.compfused.com/thumbs/88dodgearies_87.jpg

Also, ford guy I am surprised you haven't found any sales literature that includes the K. Just a minute of searching and I've found this:

http://www.lhmopars.com/MOPAR_Ads/81kcarad.jpg

and multiple commercials that refer to it as "Reliant K"

http://www.youtube.com/watch?v=wqKW6X1ayig

http://www.youtube.com/watch?v=puqtHFBJkDk

http://www.youtube.com/watch?v=F5SFuGetENE