Unfortuately I'm pretty sure they're all real reported stories. In one case the man asked to move away from his own children was Boris Johnson, the mayor of London[1], when he was an MP in 2006.
If you are a grown adult male in the USA, you will have experienced this. People believe these stories because it aligns with their own personal experiences.
So while few of us have actually been arrested for talking to a minor, and definitely very few have ever had to deal with the police over this, a large portion of us have felt the accusing stare for daring to interact with a child. We've felt the suspicious eyes of every single mother on us as we jog past a playground. We've seen our colleagues and acquaintances make paranoid, disparaging remarks about strangers around their children.
We're not scared of children because of a few scary stories in a few newspapers - we're scared of children because this happens incredibly often and the scary news stories demonstrate just how far these situations can escalate out of control.
All it takes is for one person getting burned to affect their entire social circle. Every person who's been shouted at for trying to help a kid has probably told everyone they know about the event; at that point, none of them are likely to help.
This is especially notable in the social media heavy environment we're in now. I personally know someone who got shouted at because he led a kid to customer service so their parent could be found; posted the event to Facebook, and now everyone he knows (who read the article) is going to be a little less likely to help.
There's a reason Good Samaritan laws had to be put in place; people have been prosecuted for attempting to help others in good faith, and that led to others not trying. Shitty situation, but that's how it goes.