Maybe it depends on who you're dealing with, but in my experience teenagers these days are a lot savvier about these things than the typical people in my (30+) cohort are. (They kind of have to be, no? They actually have parents and teachers snooping on them in their real lives so it's a more concrete concern for them.)

This is one of the reasons kids gravitate to Snapchat more than Facebook or Instagram after all: posts on there expire. They have a 'right to be forgotten' by default that they don't get with the other services. So I'd say they still care about keeping personal information personal, it's just motivated by different concerns than it is for the 30+ demographic since they don't have as much sensitive health and financial information floating out there.