For trash mobs, yes, in almost all cases these should never be an issue post 40, even without a tank since a party with properly geared DPS will kill most singular trash mobs without dying faster than they can be healed (about the only issue is multiple mobs in some dungeons like stone vigil). I don't think anyone was ever saying to NEVER heal people other than the tank. But there is a distinct difference between the two situations:
Given a standard opening: Tank marks mobs and pulls a group of 3 opening up with 1 shieldthrow/tomahawk against target 1, then following up 2-3 flash/overpower as the pack gets to them (and ensuring that every mob in the party has been tagged by atleast 2 enmity skills) before starting combo on target 1.
Situation 1: DPS waits until the flash/overpower before attacking target 1 (optional sleep on target 2 or 3). As target 1 gets below 5% tank flashes/overpowers again before switching to target 2. DPS finishes with 1 and attacks target 2 which the tank has already had time to build up more than sufficient enmity on. 2 falls similar to 1, and tank continues through rotation. In this situation, it is nearly impossible for the tank to lose agro against any of the targets unless the DPS is heavily geared for that dungeon.
If agro is lost (no fault), target 1 will usually die fast enough since everyone is focused on the same target that us usually at low health. In being only 1 out of the three hitting the DPS, it should not be any issue to simply keep everyone topped up. In this situation, the best thing the tank can do is maintain damage on 1 while keeping enough enmity built up on 2 and 3 so that the healer does not pull agro from healing. Unless there are more than 4 targets in the pack, mp should not be an issue for the healer no matter how much healing is being done since the tank should still maintain enough agro on secondary targets and be able to recover quickly as soon as target 1 is dead. Healer should focus on either keeping all party members alive and trying to separate enemies with knockback/sleep.
Situation 2: DPS attacks immediately after shield/tomahawk using as many skills as possible (or attacks first), uses AoE on all targets, then runs around like an idiot when they draw agro while they keep attacking with everything they have (using AoE attacks as well as single target attacks). Unlike the previous situation, the DPS usually has full agro from multiple targets, and even the primary target has nearly full health. As the DPS runs around chaotically other characters have a harder time hitting with their skills, often getting interrupted because the DPS has moved too far away to be healed, or has run behind the back of the healer.
In this situation, it is nearly impossible to recover without either letting the DPS simply die, or extensive use of CC. A healer spamming heal on the DPS can still probably keep that DPS alive through smaller fights (especially if they're well geared or lancer and the target remains still), but usually ends up pulling the other two targets onto them unless the tank has been using flash/overpower repeatedly, or CC was used without being interrupted by AoE spam.
It is in situation 2 where you should just let the DPS die and yell at them for not knowing what they're doing. It is situation 2 that leads to party wipes against bosses when the rest of the party is not as well geared. It is situation 2 where even the best tanks and healers tend to get annoyed because it is entirely preventable.
We are not talking about routine grind runs here... We are not talking about boss rooms where the additional mobs that spawn are usually a weaker variety that is specifically designed to be handled by anyone. We are talking about standard trash pulls in story dungeons where not every member may know the dungeon perfectly or be properly geared. This is where most of the bad DPS tends to occur and elitism of "I just won't run the instance with you" is not as much of an immediate option. Try making a new conjurer with level 10-16 equipment and run one of the first 3 instances sometime... You will see this sort of thing happen again and again (in addition to tanks that don't use skills (but that is a different matter though similar))... and not have the luxary of wearing equipment 10-20 levels above the dungeon. Unfortunately, this sort of behavior tends to continue well into dungeons 30+ until the healer and tank decide it's just easier to quit and requeue.