But there is indeed a built-in hash randomization mechanism

We're talking about key orderings. It doesn't matter to this conversation whether bucket selection is random or not.

And this mechanism is clearly documented in perlsec and perlrun.

I've already refuted that. In fact, perlsec says exactly what I said: Also note that while the order of the hash elements might be randomised, this "pseudoordering" should not be used for applications like shuffling a list randomly.

As for perlrun, the passage to which you link doesn't explicitly mention changing key orderings at all. It is not the purpose of the feature to alter the key ordering, much less making it random.