How to add headers to outgoing email?

Thanks to the above, I’ve realized my central mistake — I didn’t quite realize that the arguments being passed in were a multi-dimensional array.

For now, I’ve re-implemented the function thus:

function ws_add_site_header($email) {
    $email['headers'][] = 'X-WU-Site: ' . parse_url(get_site_url(), PHP_URL_HOST) ;
    return $email;               
}

My reading of the wp_mail() source (see: https://core.trac.wordpress.org/browser/tags/4.4.2/src/wp-includes/pluggable.php#L235) leads me to believe that the headers component can be an array, or a big string, or possibly some horrific mish-mash of the two, but that using an array is probably the safer/more correct option.

I do like the various phpmailer answers, but it just seems a bit cleaner to try to do things using WordPress’ built-ins.