Not exactly. You can request a site to erase all the data it has on you, but not that they erase the memories of everyone who has seen this data. How is this any different?
Your tone implies you're serious, but I struggle to believe anyone could possibly equate persisting digital media with recalling a memory.
In case you really need an example to elucidate, consider reproducing an image. A scraper can quite literally accomplish that, trivially; a great artist would still be limited in multiple facets of the recreation, such that even one with the best memory and hand would find themselves far short of pixel-perfect.
I wonder how we would regard a person who could reliably perform such a feat whenever he pleased. Would we sterilize him, lest he give rise to a bunch of cute little privacy-invading monsters?
If the feat you mean is to perfectly recall disparaging information they see about people on web sites, we already have people with quite good memories. Irrelevance usually keeps them from bringing up the details of strangers' lives on a regular basis. If the juicy details are about friends or acquaintances, well, it's very easy to destroy one's social position - at least, with non-toxic people - by endlessly and tiresomely discussing other people's misfortunes or mistakes.
How many of them saved it and then reuploaded it elsewhere? Sorry, but talking about protecting the privacy of people who upload things for anyone to see just seems silly to me.
So at which scale does the copying of data lower privacy, such that humans looking at it and potentially screenshooting it doesn't, but automated processes copying it does?
No, but since we are talking about laws, it is important to define the point beyond which a kind of behavior becomes unacceptable, or at least some set of criteria to determine when a specific instance is beyond that point.
In case you really need an example to elucidate, consider reproducing an image. A scraper can quite literally accomplish that, trivially; a great artist would still be limited in multiple facets of the recreation, such that even one with the best memory and hand would find themselves far short of pixel-perfect.