I remember listening to a radio item about paedophiles, in the wake of a big scandal, a so-called child protection expert was telling everyone not to overreact, paedophiles were 'extremely rare' and we'd all be doing our children far more harm psychologically by giving them the impression that there were abusers everywhere who were out to hurt them. 'Just think back to your own childhood,' said this 'expert'. 'How many instances of actual or potential abuse can you remember? For the vast majority of us, it will be none.'
But that was bollocks. I thought back to my own childhood, and after about 5 minutes I made a list of 6 instances, ranging from Sunday School teachers putting their hand on my thigh (while reading me Bible stories!) to a schoolteacher prosecuted for what was then euphemistically known as 'interfering with boys'. The school lied about it, just told us he'd left. And a Bible Class teacher constantly telling me to stay behind after class (conducted in his house) because, in his words, I was 'in need of extra spiritual guidance'. I'd never really thought about it before but it shocked me - I had primary school-age kids at the time - and I realised these experts were talking nonsense.
On the subject of sleepovers, of course you can't always tell whether a DC's friend's parent is going to turn out to be a paedophile, they're not all going to look like drooling pervs, but we do have ears & eyes in our heads for giveaway behaviour and talk. My OH has excellent instincts for this kind of thing, she got a lot of unwanted attention as a teenager from older men & I guess that is an education. So I would say always meet them, talk to them as much as possible, make them feel at ease, you learn so much more about people when their guard is down.
But by far the best defence is arming your kids against the threat. We had big discussions about this, about what good grown-ups would do, and what they'd never do, like the 'help me find my puppy' example upthread, and the crucial 'no good grown-up would ever ask you to keep a secret from your mum & dad'. We'd do imagined scenarios involving both strangers and people they knew. And they weren't scary, put-fear-into-them occasions, on the contrary they'd be quite ribald, we'd have a good laugh, odd as that sounds right now.
We only have boys so maybe this works better than with girls, but I can't help thinking that the attitude boys took towards it when I was a kid - suspect teachers were identified with mutterings of 'Bums against the wall, here comes Mr X' - kept us safe. Downside was, I never told my parents about dodgy Bible class teacher's approaches, the potential embarrassment was too awful to contemplate. And, back then in the 70s, grown-ups might not believe you or sympathise. One of my strongest memories is of my parents talking with my uncle, who was a policeman, about a friend who (I think) had been arrested/convicted for 'kiddie-fiddling' (another charming 70s euphemism). And they were all sympathising with the FRIEND, how awful it was for him, how his career was in ruins and he'd have to move away. The kids, oh they're resilient, they'll put this behind them.
So YANBU. Personally, I assume roughly one per 500 adults.