"The plural of anecdote is not data"

I was recently involved in a situation where an unsound reasoning prevailed. Here it is:
I was recently in a board with many people discussing about a decision that us, as an institution, had to make. Actually the decision was almost taken, but I raised the point that, in my opinion, it was inconvenient to proceed. I defended my point quoting the institution philosophy and statistics that suggested that this course of action was a waste of resources. However, some people started to object my data by telling anecdotes that apparently confirmed the decision. Particularly I was puzzled at one person that said to me: "but there are exceptions to what you say, for example, once I met someone...." and started another anecdote. So I told her "hey, but you're basing your claim on an "exception" as you said!" It didn't matter, my point had less argumentative weight for her, than the anecdote.
Finally the decision was taken, the "anecdotes method" prevailed. So I was puzzled by how we can sometimes rely on such logic of passion-driven arguments rather than logic-driven...
This method is just a faulty logic that relies on many fallacies such as: faulty & hasty generalizations, and cum hoc ergo propter hoc nicelly summarized as:

"The plural of anecdote is not data" :)