I don't think I quite understand how standby duty works; Devil's Advocate mentioned in what I imagine is a fairly typical story that he had been up since 6am one day until about 2pm the next. But his standby time didn't start until 5pm.
So, we have an 11 hour period - presumably your day off - before any sort of actual duty time starts in which to do what you want. You can, if you wish, sleep, but I suppose most would rather use their time off productively.
Point is, though, if you don't use those 11 hours to sleep, and then wind up forming an integral part of a bridge support on your way home the next day, whose actually to blame? You, for not sleeping, or the airline for forcing standby at the end of your only time off? Or both?
Answers on a postcard...