Tony may have made some precautions to prevent theft which was put it all in his head which gives newcomers, when it comes to higher ups, like Osborn a problem since there's so many superhumans who could easily hide themselves like Peter Parker, especially if they don't know that their information has been lost, but I'm sure during the process of registration that someone in Hydra intervene to make copies before it entered the system which had fail safes that were revealed when Osborn tried to access them. Tony has always been good at underestimating people and overestimating technology, especially if it's his. It's no doubt why Norman got him good.
Only the ones working with The Initiative or got arrested would be on file, while people who want a normal life, and in the new world order there's probably a lot, would be missing.
...if they had tried to access it the system would have been wiped earlier. Tony specifically did NOT allow SHIELD access to his system...so Hydra couldnt use their SHIELD links.