Here's the way I see it, a station may originate programming or lease their HD channels. They could delegate that to an AM station, owned by them or leased to an AM owned by another party. The translator rule of thumb is you must have an originating station to translate. Some translators simple repeat an HD channel. There are certain translator rules that apply. Now, a translator acquired by an AM for the purpose of carrying the AM signal is stuck doing just that. The translator in this case is glued to the AM station that acquired it.
A translator designated as non-commercial, I believe, cannot be commercial even if leased. I suppose if on a commercial channel they might request permission to classify it as a commercial translator