I think that's more of a relative impact. When you have just one measurement, you know it's not particularly reliable. When you have a bunch, we are conditioned to think it's more reliable.
So in the latter case, the distance between its reliability and its perceived reliability is greater than in the former case.
I agree with you, that it has to do with perception of reliability. However, the article seems to state that there is an actual greater error with more inputs. That's what I don't understand.
"We cannot remove the error by adding more data inputs and averaging them out, and doing that actually makes the error bigger."
I don't see how it "makes the error bigger". Maybe I'm being too literal and the writer is truly referring to the perception of the results carrying more weight, and therefore having a "bigger error".