The problem is that you cannot (yet) share a nested references using threads::shared.

What you are sharing is not a hash but a scalar $HSH2. You are then

1. auto-vivifying an anonymous hash,
2. assigning a reference to that hash to $HSH2
3. auto-vivifying another anonymous hash
4. assigning the ref of that to an element of the first anon. hash.
5. Assigning your string to an element in the second anon. hash.

Too many words, but your 2 lines of code

our $HSH2 : shared = ();
$HSH2{123}{456} = "foo.xml"; # fails
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Is equivalent to

# Why initialise a scalar to an empty list?
our $HSH2 :shared = (); 

# Assign a ref to an anonymous hash
$HSH2 = {};             

# Assign a ref to another anon. hash to a new element of the first.
$HSH2->{123} = {};      

# Assign a string to an element of the second.
$HSH2->{123}->{456} = 'foo.xml';
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threads::shared only allows you to share a single level of shared structure, and this is three levels deep, hence the "Invalid value" .

Not a very good error message. It ought really read something like:

Assigning a reference to an element of a shared hash or array is not allowed.

I'm also not certain that sharing an our'd variable is a "good thing", as it is a lexified global. May be fine, but I've never tried it and it gives me an uneasy feeling.