...and it prints 'link updated...' like it should, right?

You call the mirror method from the Module LWP::UserAgent.pm/WWW::Mechanize:

sub mirror {
    my($self, $url, $file) = @_;

    my $tmpfile = "$file-$$";

    rename( $tmpfile, $file ) or die "Cannot rename '$tmpfile' to '$fi
+le': $!\n";
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