Hopefully the ARC will come out the new duty regulations soon to make this less of an grey area. I have heard maybe sometime late this year.
It might help if you have your CP read FAR's explained, especially page 135-183, FAA Chief Counsel Opinions
" The agency has interpreted "duty" as including actual work for a certificate holder or present responsibility for work if the occasion should arise"
"The agency has interpreted provisions substantively identical to FAR 135.263(b) to the effect that a flight crewmembers receipt of one telephone call from his air carrier employer during a required rest period does not violate a regulation such as FAR 135.263(b)
At my current operation we work on the basis that "on call" is not rest, so they cannot keep us on call all day and then give you a flight late that night.
We asked the companys aviation lawyer about the issue and he indicated he certanly would not want to try a case with an accident/ incident if the company had pilots on call 24/7.