Not always (as long as you're talking about something they are in possession of, you're right if you mean you can't prove that you don't have some flash drive hidden somewhere but, then again, it need not be encrypted if they don't have access to it).
To start simply, it's certainly possible to prove that a disk installed with a base install of an OS (and then never touched) contains no encrypted volumes if all of the remaining blocks are empty. Every file can be compared to a known good copy and if there's no other data anywhere on the disk then there can't be anything hidden on it.
From there it's a case of proving that each bit of extra data on this disk relates to a file available under the OS or a fragment of such a file (now deleted). This gets progressively harder the more the disk has been used.
It impossible to deny this when you have a GB+ sized area of unpartitioned data (or unmounted partition) containing seemingly random noise. Or a similar GB+ sized file that you cannot demonstrate to be something benign by unpacking/decrypting/etc. "It's a file of random noise I generated" is going to set off the alarm bells.
If I remember correctly, when you buy a blank hard drive, and then format it, the formatting tool does not zero out the entire partition. The empty space left after a base install of an OS is note literally all zeroes or ones, it's random noise.
