A PuG I joined that was farming the instance in pursuit of trinkets had a discussion on this when -- through some act of a benevolent deity -- the Black Heart dropped 3 runs in a row. For all three tanks present, it was a giant relief; we had a warrior tanking for us, but our paladin has respecced DPS and I'd respecced Resto. Both the pally and I had unhappily agreed before the run not to roll on the tanking trinket if it dropped because that would have been a rotten deal for our warrior, but imagine the pally's agony when the damn thing dropped a second time and I won the roll. If it hadn't dropped a third time, he said to me later privately, this would have been his 14th group losing the trinket, either because he wasn't tanking and felt guilty about rolling, or he was tanking and someone won it for one of their two specs. I was on my 37th TotC run by that point without seeing any trinkets drop at all, and was starting to think that their existence was an elaborate prank of Wowhead's. Which of us had the more frustrating experience is up to you, although whenever I lose a roll, I think about this and tell myself -- it could always be a lot worse.
How do you determine loot priority in the age of dual specs?