The author of this post has a very young daughter. They wanted to protect their kid from bad content on the internet using the child protective services. First, they needed to make sure it was secure on the iPad.
They go through clicking all of the random buttons to break out. There are some screens that go into a a webview within the app. The author noticed that clicking on any links, in particular, Google links, allowed them to open up arbitrary web pages within this view.
At first, they thought this was just a single app that had the problem. After trying this technique on a few other pages, they found the same problem. So, they deemed this a security lapse on the iPad itself, especially since links like this on the iPhone don't work.
We don't see many kiosk escapes anymore. This was a good reminder of the trick of clicking on links.