The fallacy is this: You're not using truly accurate data in the first place. It's all self reported, which is not the best way to measure anything.
The model you appear to be using, axing an outlier, is reserved for truly quantifiable data. IE; a pool of patients with a median stay cost of 12k, but an average stay cost of 34k. That's when you axe the outlier that has a stay in the 200k range to get viable data. In less quantifiable means of analytics(polls), you should be just taking all of the data and doing the numbers. Just with a grain of salt.
The only problem here, is that you think it's important to argue over. I'm not trying to convince you to think differently, I'm simply saying I don't care to correct you, and it won't matter if I do or don't.