We humans are complex and unpredictable, because of this we feel and do stuff differently. Few months ago, I would never have done any dps as a healer. The reason is, because I was not confident in both healing and doing dps and to be honest in some dungeons, I am still not confident enough to do both at the same time.
Maybe the healer was too sensative, but we do not know how this player functions in real life, for all we know he or she tried dpsing and failed. Because he/she failed, they were not confident to dps as a healer. I have seen this happen with tanks alot. New tanks join the dungeon, they make a mistake which leads to a wipe. They get insulted and have less confidence in themself as a tank. In the end the tank does less dungeons as a tank and eventually quits tanking. This is one of the reasons why we have a lack of tanks.
We as gamers need to remember that just, because Bob is a epic healer and does extra dps, does not mean Joan can do the same. Maybe Joan doesnt want do any dps and wants to only heal? Isnt this the reason why most healers leveled a healing class? To heal in dungeons? I understand that doing extra dps as a healer is a bonus for everyone, but I can also understand that as a healer, I did not level my Scholar and White Mage to do dps in dungeon. I reckon alot of players probaly feel this way.
My rule when doing dungeon is:
Tank: Keeps agro and casts defensive spells to lessen the damage received.
Dps: Does damage (his or her best) and CC when needed.
Healer: Keeps everyone alive and manages their MP pool.
Any extra dps from both tank or healer is a EXTRA, if a Dps player does some healing or tanks a mob for some reason (tank is dead), then this is also a EXTRA. When players do this, I give them a big thumbs up! But this is not a requirement when doing a dungeon its just a EXTRA BONUS to clear the dungeon faster.
The healer from OP's dungeon might have been oversensative, but aslong we dont have the full story, I can not make a judgement based on 1/2 of story.