When I say this, people are taking it way too literately. To refresh:
a) There are three "roles", Tank, Healer and DPS. If you step outside that role, you are taking ownership of the party failure. This is not suggesting that Healers should not DPS and DPS should not heal themselves, but rather if you step outside the role, you are still responsible for your role. With healers this is far more critical.
b) A healer that is DPS'ing when there are no healable targets is adding to the total DPS. A healer that is DPS'ing while other players (DPS/Tank) are healing themselves are subtracting from the total DPS. Hence again, you do NOT DPS while there are healable targets. If players were playing the dungeon instances with the minimum gear requirements instead of maximum, they would have no opportunity to DPS period, and instead need to conserve MP.
c) There is a certain threshold at which a healable target "needs" to be healed, and the goal posts move the farther away from the minimum gear requirement is. If the entire party is minimum gear, then overpulling would not even be an option, as MP would be exhausted between pulls. People keep forgetting this because parties are often comprised of over-geared tanks and over-geared healers with minimum geared DPS in the low-level dungeons. When it's reversed (minimum geared tank) the healer has spend a lot more time healing the tank, and thus has less opportunity to DPS. A minimum geared tank may have as much as a 50% difference in HP compared to a maximum one. That changes the healing requirements significantly when the amount of damage they take goes from 5-10% per hit to 40% per hit.
d) The dungeons are not designed to be speedpulled. You do so at your own risk. Healing requirements scale linearly, where as damage in AOE scales exponentially. So if each mob hits the tank for 3% damage (3 mobs), a regular pull might incur 10% damage every 5 seconds, but a speed pull of 10 monsters takes that to 30%, and some insane "to the boss room door" pulls can easily flatten an overgeared tank with bad timing of all the mobs striking at the same time. But two DPS timing their AOE's at the same time are doing damage to all 10 monsters at the same time. The more you pull, the more vital it is to avoid AOE's yourself, especially anything that stun/paralyzes (eg Morbol's.)
e) Please play with randoms in the Duty Finder if you think healing is too easy. I assure you that the only reason healers might be bored is when the party is actually good enough to not require as much healing as a band of newbies. Take that opportunity to DPS rather than stand still. You're never required to, and anyone who throws a fit about you DPS'ing or not DPS'ing is a poor player to begin with.
A lot of misconceptions about FFXIV come from players who apparently played WoW or GW or some other MMO where basically everyone is a DPS and few people pick healer roles because the healer role is too squishy, and other healing mechanics (eg pots) are cheaper and lack penalties. The Tank who chainpulls is an example of bringing bad habits from one MMORPG to FFXIV.
If you are going to play a game, you first play it like the developers intended it, and then when you see opportunity for emergent gameplay, that doesn't break the intent of the game mechanics, you take advantage of that. Trying to go straight to minmaxing every GCD just because it's there, is not not smart or efficient gameplay, and certainly isn't fun to play with party members who expect a pro every time.