You say we can’t predict the future, but can we “predict” the “present”? That is, let’s say I manage to talk my way into getting a sit-down with some bigwig General, then calmly state - “Oh, I know the Roswell thing was just Project Mogul.” (Or whatever super secret project the person might know about, but which I shouldn’t know about.)
This obviously has a few problems. One, I have to get access to the right people without being rejected as a crank by his low-level people who don’t have any idea what I’m talking about. Two, if I do convince some important person to let me have five minutes of his time (say, by posing as a reporter doing a story on important people), there’s always the risk of them thinking I’m a communist spy as soon as I mention details of a Top Secret project.
But, if someone knew enough about secret shenanigans back in the day, they might be able to eventually convince someone that they’re really from The Future. At some point, time travel would be a better explanation of their vast knowledge of things they shouldn’t know than that they just happen to be the greatest spy of all time who suddenly turned themselves in for no reason.