Well, for the uninitiated, this merely makes the dance between A&E and Robertson a two-step dance instead of a one-step dance. Gurney Productions (owned by
Scott Gurney) most likely created the concept for the show, signed Robertson (and the other cast) to employment agreements, filmed a pilot episode or two, and then took them on the road to see if they could sell the show to someone. In this case, A&E bit and agreed to buy the show. A&E and Gurney Productions would then have entered into their own agreement governing the production, transfer, and distribution of the show (at the least; there may have been other issues that were addressed in the contract).
Now, in terms of morals clauses: (1) unless Gurney Productions is a neophyte startup run by someone who's never done production and not had proper legal advice, there is a morals clause in the contract between Gurney Productions and Robertson that gives Gurney the discretion to terminate Robertson for the sort of conduct that is usually covered in morals clauses,
and would include conduct that any third party purchaser of Duck Dynasty objected to, and (2) there is almost certainly a morals clause in the agreement between Gurney and A&E under which Gurney agrees to remove from Duck Dynasty any cast member whose conduct falls under that clause, as determined in the sole discretion of A&E (there might also be some other tempering language, so that A&E cannot simply act arbitrarily and capriciously - i.e., a form of good-faith provision).
Under a two-step arrangement like that, once A&E decided that Robertson's conduct was objectionable, it would have exercised its rights under its agreement with Gurney Productions to demand that Gurney remove Robertson from the Duck Dynasty show - to put him on "hiatus" - and Gurney, in turn, would have exercised its rights under its agreement with Robertson to remove Robertson from Duck Dynasty because his conduct violated the morals clause. As for whether Robertson continues to get paid by Gurney Productions even though he's on hiatus, that depends on the relative bargaining strength of the parties when they originally drew up Robertson's employment agreement. My guess is that since Robertson was an unknown before Duck Dynasty Gurney was able to get language into the employment agreement that gives them the discretion to stop paying Robertson if he's removed from the show because of a violation of the morals clause.
At the end of the day, Robertson was forced from the Duck Dynasty show because A&E objected to his conduct and had the necessary power under the relevant morals clauses to legally force him off the show.
