This claim surprises me, and does not match my experience.
- Postfix uses smtp_tls_cert_file for the client certificate to use for outbound connections, and smtpd_tls_cert_file for the server certificate.
- Exim similarly configures the smtp client transport certificate separately from the server certificate.
- Apache httpd configures client certificate for use in a reverse proxy to another server via SSLProxyMachineCertificateFile, though its server certificate is configured in SSLCertificateFile
- Nginx similarly uses a separate configuration property proxy_ssl_certificate for how to authenticate using a client certificate as a reverse proxy, not the normal server certificate settings.
I'm sure there's some software out there that will use the server certificate by default when acting as a client, but I'd expect that most of the time it'd be possible to configure it otherwise.