The issue is that many of the things people share on Facebook/Twitter/etc are actually "taboo", and people's evaluation of them is just wrong. As an example, the story of Justine Sacco, a person who would arguably be even more aware than the average of the impact of public statements, still did not manage to correctly evaluate that the things she was sharing on Twitter would lead to a serious backlash and witch hunt against her.
The worst part is, you won't necessarily get instant feedback, like Justine did. You may post something "among your friends"(in reality, publicly on Twitter), all your friends may agree with you, and then several years down the line you will be judged by a completely different social group, looking through your records. We don't tend to accommodate evolution in people's beliefs as much as we do for ourselves - try the defense "I'm not that kind of person anymore" to strangers and see how often it works out(no need to try on your own, just check out how easy convicted felons have it when trying to reintegrate into society).
I mean if you did make "dick pics" and were bothered about people seeing them then you likely did it wrong and your ISP had access and your phone provider had access and your backup service provider had access. At that point, why would you - short of guilt - be bothered that the government might have potential access in a situation where you were accused of a crime. If you're on the "nothing to hide" side of things, how does that push you to any other position.
In short, it's pithy, and Oliver probably made good talk-show level comments but I don't see it as really being a persuasive way to couch the argument for greater privacy.