A system needs to be able to remember what it is supposed to forget in order to make sure it is forgotten.
Imagine a waiter robot that is supposed to go into a room and make sure it gets everyone's order:
a) Enters room, goes from person to person, asks drink preferences.
b) John Doe tells robot: "I don't want you to track my preferences. Forget everything about me!"
c) Robot obeys and continues on.
d) Prior to exiting the room, the robot verifies it has gotten everyone's preferences.
e) Robot sees John Doe. Robot has no record of John Doe because it has forgotten everything about John Doe. The robot must get the preferences of everyone in the room.
f) Robot asks John Doe for his drink preferences.
g) Goto b).
The systems have to remember that they aren't allowed to (re)learn the data that they are supposed to have forgotten, which means they cannot completely forget things - the information is always there.