Apparently the brain, as it has evolved, stores information in a way that probably makes it hard to "program" people to inherently possess any explicit knowledge as if it was taught to them in school. Genetically imprinted understanding would rather manifest itself as more or less instinctual behavior, much like how beavers construct their dams or termites build their colonies.
While this might be enough to kick-start a technologically advanced civilization, there is a problem: such behavior might be hard to contain and keep completely secret. People might engage in forbidden activities without even knowing why they are doing it.
How to prevent it from happening while the Neo-Luddites are in power? If they are devoted enough to their cause, they would probably spot early attempts at some point, and they would try to make it stop before it gets out of hands. What would prevent them from trying to eradicate everyone, just to be safe, who showed any propensity towards anything technological? They don't need to know where it comes from, they might just as well think that some understanding of technology still remains, and some people pose a danger to their cause.