Just about sixteen years ago they were everywhere and ran the galaxy. Even Lil’ Annie knew all about 'em! Even if (maybe especially if) there were huge galaxy-wide book burnings, ban on all evidence, believers rounded up, ect., plenty of people would remember it and there would be plenty physical evidence to back it all up.
There just isn’t enough time between ROTS and ANH for me to buy any of it. I’m just not willing to believe that everyone in the galaxy is that stupid.
Like CHEWBAKAspelledwrong said, the prequels suck.
That does leave Ben though. He’s the right age for the accepted timeline. So is Vader, come to think (what I’m saying is that they’re human and the timeline is compatible with human lifespan). It’s probably more a problem of misrepresenting the Jedi in the prequels than a timeline issue. They should have been a more covert and mysterious organization. I think benevolent, organized, monkish vigilantes would have been better than seeing Yoda taking meetings with Senators.