In that case make it required by law to publish apology following same format as was the original article. Did you print the false claim on title page of newspaper? Same place, same size for and apology. Same with web articles. That should at least make it searchable by engines.

That information has already been dissiminated. And usually has a higher hit-rate than any correction.

We know employers can and have discriminated against individuals where convictions have been overturned.

Relevancy is a problem that firmly falls under Google's responsibility... and businesses must be punished for discriminating over incomplete background checks.

However, I don't think the false conviction should be hidden - what if they were guilty and there's a crimes down the road? That information could be useful for the public.

Saying "X was convicted of Y" is not a "false claim," when X really was convicted of Y. If X's conviction is later overturned, that's additional information, but it doesn't make the original information false.

Nobody owes anyone an apology.