A right to be forgotten - that is, not to be mentioned somewhere - looks more like a negative right, not unlike a right not to be mugged or not to be photographed in your own bathroom through an open window. A right to be remembered would be a positive right - not unlike a right to be employed or fed.

(You could say that "forgetting" published material requires action and not inaction - but so does editing out someone videotaped in their own bathroom through an open window, and so does not running over pedestrians, strictly speaking; generally as programmers know following rules to not do something requires some sort of computation which is a form of action... but that means inaction takes action and then all rights are positive.)