I think as the FAA reviews its rest requirements for pilots, that this type behavior will be reviewed.
At the airline I work for, "jumpseaters" are observer members of the crew....As the FAA scrutinizes aspects of crew rest, I believe they would be justified if they said that jumpseaters are de facto members of the crew, therefore they are not resting, and legal duty limits would apply to that crewmember.
If that would come to pass, the scenario of jumpseating on a red-eye to check in for duty on the morning of arrival would be problematic from a duty/rest perspective, and that responsibility would and should fall on the jumpseating crewmember, deservedly so, in my opinion.