Replace eval $code with print $code and we get

$hashref->{'globalkey'}->{'key2'}->{'key3'}->{'key4'}='ARRAY VALUE';
$hashref->{'globalkey'}->{'key2'}->{'key3'}->{'key4'}->{'key5'}='ARRAY
+ VALUE';
$hashref->{'globalkey'}->{'key2'}->{'key3'}->{'key4'}->{'key5'}->{'any
+ arbitrary number of keys'}='ARRAY VALUE';

use Data::Dumper;
print Dumper($hashref);
__END__
$VAR1 = {
          'globalkey' => {
                           'key2' => {
                                       'key3' => {
                                                   'key4' => 'ARRAY VA
+LUE'
                                                 }
                                     }
                         }
        };
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Add strict/warnings and we get

use strict;
use warnings;

my $hashref;
$hashref->{'globalkey'}->{'key2'}->{'key3'}->{'key4'}='ARRAY VALUE';
$hashref->{'globalkey'}->{'key2'}->{'key3'}->{'key4'}->{'key5'}='ARRAY
+ VALUE';
$hashref->{'globalkey'}->{'key2'}->{'key3'}->{'key4'}->{'key5'}->{'any
+ arbitrary number of keys'}='ARRAY VALUE';
__END__
Can't use string ("ARRAY VALUE") as a HASH ref while "strict refs" in 
+use at - line 6.
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That explains everything nicely :)