Right. You ought to do that for the other lexical variables too, to avoid similar problems (though with them being all scalars and you not calling any other code likely to change them, you're safe for now). I would write that subroutine more like:

sub run_query
{
    my ($query) = @_;

    my $sth = $dbv->prepare( $query );
    $sth->execute();

    my @new_row;

    while ( my @row = $sth->fetchrow_array() )
    {
        my $string  = join( ',', @row );
        $string    .= "\n";

        push( @new_row, $string );
    }

    return @new_row;
}
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I removed the code after the return call because Perl will never execute it. (Further, if you exhaust the result set, as this code does, there's no need to call finish().)