I actually read a book about this a while back. They employ tactics of "grooming" which is basically brain washing. Of course, it never starts out with "hey, take off your shirt". Usually it starts out with innocent conversation, usually he won't disclose his PI(personal info like real age, etc) strait away, just as a young girl isn't going to straight-away give out her phone number or school info.
... and once he's sure he's gained the the girl's trust, she'll learn things like he's older, like a lot older. But! That's okay because older guys are sophisticated and he knows she's mature enough. What a coincidence, they have the same taste in music (they both know Justin Bieber's music is actually really good a people should just give it a chance before they judge it). It must be fate. She makes him want to be a better person, he understands her problems at school and with friends...Her parents freaked out about something no big deal, but he knows that her parents just don't get cool things, just don't get her, that's why they cannot find out about "us" because they totally wouldn't get it, they'd probably freak out, she'd definitely get in trouble. So she never mentions it. He tells her how gorgeous she is, how she makes him feel things, he thinks about her all the time (and at this point, she's thinking about him all the time, too) he wants something so much...what is it? To see more of her (sans clothes). ...maybe he got her phone number so they can text each other good night, maybe he got her address so he can send her a B-day gift! It's no biggy, he lives all the way across the country (and he's proved it too) so it's not like he's going to do anything else with it.
...now, say she gets wise at some point - got a bad feeling in her gut. Maybe she openly ponders if they should really be talking, or she flat out says no to him. He gets impatient/mad... that's when manipulation happens (not that it hasn't been all along). He threatens self-harm, or maybe he's doxxed her (or pretending to) with what she's already said casually. He threatens to harm her, her family, he'll show up, her parents will find out. Any of this would scare the crap out of anyone, a lot of this you'll find in other answers in this thread. Not to mention, doesn't that sound familiar to crazy ex behaviour? Same manipulation, different audience.
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TL;DR: 13 years old is NOT old enough to know better! Nor is 16, nor is 19, nor is 25, etc. At any age 30 yr olds/40 yr olds/50 yr olds fall for it, (via international lovers' scam) because it is BRAINWASHING that can only be combated with open communication.