Is being wrong forgivable when you admit fault?

I’m specifically referring to responding to statuses on social media. If one reads a click bait article title and reacts rather than investigating thoroughly. To only have pointed out to them “actually that is not the cause… because…”

Hypothetically if a person was to respond by saying “actually you are correct, that was an error on my part.”

Some people are of the opinion that making an inaccurate statement online should result in a person to never be trusted again. While others feel that if the person admits the mistake, they at least have the integrity to be honest.