I'm going to take a guess, and say that while you may be searching the correct database (i.e. nucleotide), you are likely using the wrong id to perform your search.

Using an id of NC_000016, results in fetching sequence data with the annotation that you expect.

The code below will result in a fasta file that contains NC_000016 Homo sapiens chromosome 16, GRCh38.p2 Primary Assembly in the header. It may take a while for the script to finish, since this is a big sequence. The output.fasta file is around 100 MB.

#!/usr/bin/perl

use strict;
use warnings;

use Bio::DB::GenBank;
use Bio::SeqIO;

my $output = Bio::SeqIO->new(-format=>"fasta",-file=>">output.fasta");
my $gb = Bio::DB::GenBank->new();
my $id = 'NC_000016';
my $seq = $gb->get_Seq_by_id($id);
$output->write_seq($seq);
exit;
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