A plurality of anecdotes sampled without bias?

That's the problem: interesting data points become anecdotes while uninteresting data points don't, which is why you can't reconstruct the data from the anecdotes.

Right, but people always make the statement without qualification. So just saying "the plurality of anecdote is not data" is simply not true. You can say "may not be scientific" or "may be incomplete" but to say it is not data is incorrect.

A problem with your statement is that you can substitute "data" for "anecdotes":

A plurality of data sampled without bias?

That's the problem: interesting anecdotes become data while uninteresting anecdotes don't, which is why you can't reconstruct the anecdotes from the data.