Successor plan rules and one participant plans

I have a scenario where a one participant plan recently terminated their plan and is hoping to start a new 401k plan. Do the successor plan rules apply here and must the client wait 12 months before establishing the new 401k plan?

Under what circumstances was the previous 401(k) Plan terminated?

As a general rule, my understanding is that the successor plan rules apply to all companies sponsoring a 401(k) plan. I haven't seen anything that would except a single employer plan, but I could be wrong.

The previous 401k was terminated after the client learned that they were a member of a controlled group that already had a 401k plan in place. 

Wouldn't the 401(k) plan sponsored by the other controlled group member be a successor plan to begin with, making the first plan termination problematic?

I think they apply all the more to a one-participant plan, because that is where there would be the most potential for abusing the plan as a temporary "piggy bank."