Actually there are a lot of bad tanks in this game and it is fairly easy for a well geared DPS to draw aggro from most of them just by using their standard rotation without buffs like Raging Strikes. Trash mobs don't hit hard, I have cleared half of AK with a 3 man party missing a tank, so there is never an excuse for not healing a DPS who draws hate. Never. The DPS should be trying to make the tank and healer's life easier however by popping defensive buffs like Manaward when they draw aggro or DPSing the second mob if they know they are about to draw hate on the main target.
At the end of the day if anyone dies to a trash mob then I question whether that healer is going to be able to heal through boss fights and most of the time they can't.