I've always found it remarkable that all these on-demand operators work the way they do when the FAA itself has clearly and specifically defined being "on call" as being "on duty", and even addressed directly FR 135.267(d), which is unscheduled 1 and 2 crew pt 135.
http://www.faa.gov/about/office_org.../interpretations/data/interps/2009/Mayors.pdf
http://www.faa.gov/about/office_org.../interpretations/data/interps/2009/Mayors.pdf