Not OP, just curious why this is being downvoted? Seems like a legitimate argument, would rather like to see the counterargument of the downvoters.
First of all, the premise is wrong. Major corrections usually receive more prominent placement and greater exposure. Minor corrections are printed in the corrections section, with stories updated online and correction notices appended.
Second, the point is not that reputable newspapers perfectly correct their readership's understanding. The point is that reputable newspapers correct themselves. Newspapers reputations are built on that honesty, and astute readers will have an understanding of a paper's track-record of accuracy and corrections. Less astute readers will rely on those that do track such things.
This is not useful most of the time. I've never seen a viral correction. Damage is done.