Well said Dan.
Folks, those of you who don't operate as crew in the longhaul area and those of you who fly substantially less than a full 900 hour roster really shouldn't comment on the management of rest patterns on the dreaded 24-hour slips.
It frequently just isn't possible to sleep on demand for a few hours before pickup.
The example Dan gives which is quite typical, ie Europe to US Eastern Seaboard with a red eye flight home after 24 hours. In that rotation, the flight home is exactly when your body is screaming at you to go to bed and sleep.
And as for those comments/suggestions to go 'crew fatigue' - it's the job, you have to find a way to cope, often by catching a half hour of controlled rest at a quiet time in the cruise in the seat, and yes, tell your oppo that you feel like death warmed up and take things slowly.
If things go wrong then the adrenalin rush will kick in and your alertness will increase immediately.
In the MEL case, it seems to me that a lack of rigour in the checking process possibly due to defficient SOP's and a possible lack of mental modelling for the take off let them down.
Bad show on the airline management though, nonetheless.
[Edited to add: 2008 = 870 flying hours, 520 time zone changes, 57 nights out of bed = lost sleep]