So my best guess as to the nature of the LA "hack" was that the students went into Settings > General > Profiles and tapped "remove" on the LAUSD MDM profile. Some hack.
The technical lesson here is this: security critical profiles never come over MDM.
At Cedars, we use the Casper Suite from JAMF Software (disclosure: they also sponsor my podcast). We deploy several configuration profiles over MDM but our base security profile is always deployed through Apple Configurator to ensure that students can't remove it.
Of course, there's a broader point to be made here too which is that an iPad that's locked down to Pearson curriculum content is probably the saddest of all iPads. The very act of giving out an iPad for "education only" purposes generates exactly the pressures that lead to breaches like this.
Fraser explains exactly what happened and how it could have been solved. Fraser and I both believe that the future is about taking the locks off the doors and educating students about responsibility (digital or physical). Before you start ripping on Apple for a 'hackable' device, you need to read this.