Local in nature would be ok if the pilot ended his trip at the away station and went to a nearby hotel. That time could (which means it would) be counted towards the rest period.
But, he isn't heading to a hotel in the case of driving back to the base. He is heading back to the base, his work place, where he would end his duty period.
Local in nature was conceived that a pilot's commute to work was part of his rest period, since it is his choice where to live and how long it takes to commute. Then, because airline crews don't end their day at their domicile everyday, the FAA accepted "local in nature" to include the brief drive to/from the hotel, as if that was his local commute. Since the definition and intepretations are based on "domiciles", that comes to mean his place of employment. In our case, our "domicile" is our base. And, transportation by the company between an airport and the domicile is not local in nature since it is required ground transportation provided by the company. So, that is on the company, not the pilot, and is considered deadhead (duty).
So, if the area manager has the on-coming pilot drive to where the helicopter is, and swaps pilots, and the off-going pilot is not back at his "domicile" but has to drive back there, it is not "local in nature".
We don't have "co-domiciles"! We are assigned to a single base, so don't let anyone waive that letter of interp at you about the Washington DC Reagan Airport - Dulles (IAD). That pilot was co-domiciled (he had two work bases). Its the responsiblity of the company to get you back to the beginning (deadheading), where your regular commute starts/ends (local in nature).