You did nothing wrong that loot was yours to win. There is no unwritten rule about loot drops when using the Duty Finder. If you need it and you can and you want it, then need it.

Other healer was just hurt because they were probably farming X piece for days and lost it when it dropped. Tough luck keep farming, that's how it works.

It took me 3 weeks to get the Healing Robe, and not once did I complain because that's how it works.

The only times when loot rules apply is when you are doing specific things if your Guild or friends and specify aspects if they are even needed, Otherwise anyone that complains about loosing loot needs to grow up, Thats just the harsh reality of the way it works. You are not entitled to ANYTHING.