You can help them find out. I'm all for letting them explore on their own, but there is another way. The BYU Family History Technology Lab has several different projects that interact with your Family Search family tree. One of them is called Relative Finder.
Relative Finder compares your family tree to various groups of famous people who are listed on Family Search; apostles, prophets, LDS pioneers, Mayflower colonists, European royalty, US presidents, anyone who has at least one line on their tree going back 10ish generations should be able to find something. Youth who do not have extensive trees are probably out of luck, but with a little bit of research they may be able to link back to a deceased relative that has a bigger tree.
|William the Conqueror, my 29th great grandfather|
How legitimate are genealogies that go back 29 generations? I don't know. Probably pretty questionable. In the end, we're all related to Adam anyway so if Amelia Earhart isn't really my 10th cousin, she's definitely in my tree somewhere else. It doesn't really matter if it's accurate or not. For youth there's nothing less exciting than their parents and if they think that their genealogy is full of people like their parents, what's the point of learning about it? The point of checking this site is to have them consider the possibility that there might actually be something exciting in their family tree.
Youth can learn anything they want to learn (adults too). If every family history experience they have is frustrating and boring, they won't come back. With so much to learn it seems counterproductive to waste time finding out that Joseph Smith is my 5th cousin 6 times removed, but it's fun. It gives them something to post and talk about. It helps them appreciate their ancestors and the other family genealogists.
Give them some time to learn that regular people's stories are just as exciting. Once the genealogy fire is lit, they'll keep coming back to it throughout their lives. It's worth it to spend a little time kindling the fire.