since I am always pathing through a reference, I apparently need to make a reference to the reference?

\$_[0] is not needed if the given (first) key is already a hashref. E.g.:

my %DATA = (3 => {});

put_element($DATA{3}, ...);
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But it is needed if the key doesn't exist yet:

my %DATA = (3 => {});

put_element($DATA{42}, ...);
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"But why doesn't my $current = \shift work? Why do I have to use my $current = \$_[0]?" Answer: If the key already exists and its value is a hashref, both possibilities work. But if the key does not exist, we have to make sure, that we really get a reference to the entry of %DATA, not the value of the non-existing entry.

sub test1 {
  my $val = shift;
  $val = 5;
}

sub test2 {
  $_[0] = 5;
}

my ($a, $b) = (3, 3);

test1($a); # $a continues to be 3.
test2($b); # $b is 5 now.
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But I could have missed something, too.