Great job on the research!As to your legality question, since Barkley was not representing itself as something it was not (ABA approved) then I do not see how Kentucky could stop it from setting up shop unless it was making material misrepresentations. There have been several lawsuits and at least one pending one by a former student pro se who claims Barkley was a RICO enterprise and engaged in loan fraud of some sort.Novus on the other hand, may cross the line into diploma mill territory which can be illegal.
Barkley had a real school with real law professors and classes and seems to have intended to get ABA accreditation.The Barkley degrees are real enough - they just are not accredited.A diploma mill awards a degree for little or no work so that the purchaser can claim they have a degree.http://en.wikipedia.org/wiki/Diploma_mills_in_the_United_States
Being incorporated in the RMI (Republic of the Marshall Islands) means nothing except someone incorporated an offshore company. It in no way implies any approval by the RMI. And I can assure you, no one from Novus is resident in the RMI. I would say it is a gray area at best - diploma mills are one reason why DL and correspondence law degrees are held in such disrepute. Places like Novus make it harder for everyone who is pursuing a legitimate DL law degree and seeking to practice law because ignorant and biased people fail to realize the difference between studying law for a degree and just paying money for a diploma.
First you need a plaintiff who has standing and the defendant can be sued in any jurisdiction where they do business if I understand your question correctly. Just not liking them is not grounds to sue.