It should not be removed from the internet, but it should be removed from google. It's not the same thing as dealing with paper newspaper. One you have to go an explicitly look for the information and browse through them to get it (and still it can escape your gaze). With google you just need to type name and surname, and everything is at your fingertips.
Either it's removing public information (censorship), or it's this bizarre stop-gap to allow people to conceal information while pretending they aren't deleting it. There's not reasonable or principled system here. Just a dangerous stop-gap measure where it seems like people are trying to delete (censor) information under the guise of individual freedom ("we're just making it harder").
I don't really buy into the middle-ground presented by this measure.
The "right to be forgotten", in that case, becomes the "right to erase history."