In short, there are many ways to give a judge the idea that the use of a hidden volume is likely (ie: check path histories for previously opened files, check temp folders, etc). Not only would these indicate the possibility of a hidden volume, but some files that were meant to be encrypted may be 100% available (eg: Microsoft Word makes temporary backups of files in your %APPDATA% folders in case it crashes and you want to recover your work; as one example). Unless one is very diligent and knows what he/she is doing with respect to encrypting data, it would seem the only safe method is to encrypt the entire disk and boot off of it exclusively, all while keeping the machine itself disconnected from the internet to avoid hacking attempts, and locked in massive safe so the authorities don't install a keylogger (application or physical device) or start taking snapshots of your disk daily to aid in cracking the password.
You may be able to secure your data, but with multiple means of data accidentally being leaked due to the OS or various applications used in day-to-day life, along with unscrupulous policing agencies allowed to overrule fundamental civil rights, it is likely that one will ultimately lose their data and/or freedom either way.

Except this isn't true of microkernel systems like Minix. And this is the point: microkernels enforce protection boundaries between components so failure and recovery become feasible. That simply isn't possible in a monolithic kernel without resorting to proof-carrying code of some sort.

after they leave the corporation.