Your brain is the "mechanism", but your neural pathways are not the same as anyone else's, these pathways are all unique due to their timing of creation. In more basic terms, you cannot have the same false memory at the same time as someone else about the same thing in the same way unless you have identical neural pathways that were formed at identical stages of your growth. Then we move on to DNA sequences and how your neural pathways are formed differently based on your heredity. Even with a centralized brainwashing program like television, if there were false memories based on this programming each incident would be unique to each individual. This starkly contrasts the reality of the billions of people who just happen to remember the exact same things in the exact same ways, not just TV shows, but very real things like the thinker statue and marilyn monroe's piercing, for which it was famous but now does not make any kind of sense being on her cheek. There is a clear and evident divide between what is now and what was, and nostalgically charged memories only uphold this obvious fact.