For the guy that's done time. Most likely he has to admit he has.
For the average person caught in this, this isn't likely to make a big difference. They can't afford the costs of trying to have their records hidden. And for the most part, no one cares, beyond the obvious.
This is about RICH, WEALTHY, individuals who have been reasonably damned, and want to hide it.
Can't sue for slander in the US if it's true.
The EU seems to have a different opinion of past records.
Not that it really maters. The EU ban only applies to EU sites. Simple enough to proxy around to get the details. It only deters the casual browser.
It's a brave new world. Despite some country's laws, you don't have the right to be forgotten. Until every country enacts such laws, you're out.
There are other similar battles, will be interesting to see which island wins.