Standby time is duty time, full stop, we used to have the same problem at my airline, they counted standby time as 'rest time'
Call outs at the end of your standby time could lead to your being awake far too long to be safe.
In this case the intervention of the FAA was a good thing..
No heroes please, in some managements world and 411 of course you are the saviour of the company if you run yourself into the ground with fatigue.
Or literally in which case they will pile the blame on you for not being more responsible.