This is due to the new verify-by-default policy in PHP 5.6. It's not set in php.ini; it's an option you can provide to fopen wrappers or stream contexts. Have a look at the options here, especially verify_peer. http://php.net/manual/en/context.ssl.php
PHPMailer allows you to set these params during the smtpConnect() method, but there is no option to pass options into the smtpSend() method, so you will need to subclass PHPMailer to get at that.
This might be an alternative: http://www.docnet.nu/tech-portal/2014/06/26/ssl-and-php-streams-part-1-you-are-doing-it-wrongtm/C0