I've read the FAQ item and I'm sorry to say that it seems written by somebody talking out of their behind, giving legal advice to boot.
Sure, once in the hands of the Russian FSB, Italian Mafia or Nicolas Maduro, any detectable amount of random data could result in torture - just to be on the safe side, maybe there is a hidden volume there after all.
But in any state where rule of law is observed, the prosecution must establish probable cause and, once in court, prove beyond reasonable doubt that the illegal act was indeed committed - in this case, failure to disclose the encryption key of a locked volume. So there must exist corroborating evidence that should exclude any reasonable accidental or normal situation that could produce the random data. For example, a border agent could testify that he saw illegal material on your device's screen and a random file could be found in your home directory. In your device history, traces to a missing volume or partition could remain etc. The defense can easily explain away a partition initialized to random, if that's what standard system tools produce in their normal configuration and no other corroborating evidence exits.
A LUKS header is a clear indication that another encryption configuration was/is used on the computer, so you would then be compelled to give explanation about it's presence, it's password, the provenance of the laptop etc. The explanations given in the FAQ (experiment, random swap) are unconvincing if they are not corroborated by other patterns, for example modification timestamps on /etc/fstab and /etc/crypttab and so on.
So the absence of the LUKS header really does fill a practical gap, and it happens that most legal systems today are squeezing harder and harder into that gap. Unlike the dubious claims in that FAQ entry, Truecrypt hidden volumes actually have established legal precedent.