No, it doesn't. If I'm running Waterworks and one person keeps sprinting ahead, grabbing Kobold aggro and sprinting back to the party because they can't handle the aggro, it does not fall to anyone else to continually clean up the mess that came from their poor decision making.
If I'm running Monestary of the Scorpion and one person keeps running into the traps, it does not fall to me to keep them healed because they do not have either a) common sense or b) evasion + sufficiently high reflex save.
If a WF of any class takes 0 ranks of Healer's Friend and takes no Healing Amp gear and doesn't bother to chug pots between fights, it does not fall to me to keep them topped off and alive through fights when they are taking more damage than they can handle.
You should make an honest effort to keep people alive - but that's true no matter what your class is. If I'm a fellow melee, I'll try to peel a couple of enemies off of the barbarian if he has too much aggro. If I notice that one character keeps dying and I'm on my own melee, I'll try to be the first one in the room so that I at least get all the "Hey! There's a PC here!" aggro that doesn't come from damage dealt. When that isn't enough and when that player doesn't seem to be making a significant effort at keeping themselves alive, then they get a free ride in my backpack.
I've been guilty of the same myself. I've gone into Epics underequipped. I've gone into quests with insufficient healing for myself when I'm on my Ranger or my Fighter. I've gone into VoD with 0 pots because I forgot that I had chugged the last of them all doing some other quest the day before. When that happens, I apologize to the group and let them know that I did something wrong and that I know it's my fault. I've *never* had a group fail to take care of me when I mention that I had forgotten something or made a mistake in what I can handle in combat. Even if if that support is just getting a free ride in someone's backpack until we get to a part of the quest where I can handle what the quest is throwing at us.
The difference is whether the player is at least attempting to taking responsibility for their own survival and success. Carry some poison pots. Carry some curse pots. Carry a disease immunity item if you are planning on running some desert quests. Carry a few Fire, Cold, Acid and Electricity resist 20 pots from the 12 in case you get stranded in a quest with a Sorcerer who took Melfs, Summon Monster II, See Invisibility and Daze Monster as his level 2 spells...
Yes, you should complain about the healer in the Shroud who let half the party die in round 4. No, you should not complain about the healer in the Shroud who let you die a second time in round 4 because you sprinted back into the fight at half health and with no buffs after you took your raise.
Each player needs to take
responsibility for themselves even when they can't keep their own red bar full from the beginning of the quest through the completion.