There's a little bit of subtlety here, but in general GP was correct in that it can be made hard for authorities two tell exactly
what changed.
Disk encryption, unlike other forms, does not have a terribly high avalanche factor when small changes are made--because it's expensive to write lots of things to disk.
However, it is possible to make a small change (as small as, say, writing the audit log file on a real successful login) that renders data completely inaccessible. Consider an encrypted disk on which you can tell the magnitude of changes on the filesystem, but not which data has changed. Let's say you have a lot (many gigabytes) of sensitive data on that disk. If a successful login triggers the encrypted filesystem to decrypt the contents of the disk using an encryption key (of, say, a 4kb length) that is stored only on that disk, then a duress code could simply destroy (or corrupt by randomizing a few bytes) that key, rendering the contents of the disk inaccessible, without writing more than a very small amount of data.
This fundamentally trades off deniability for data security: the disk would still contain all of the encrypted data and could be brute-forced, but that would be the case anyway if an image had been taken previously.
Of course, situations in which that deniability would be legally well-received are, as others here have pointed out, vanishingly rare.