If pine can't use SMTP authentication on an Exim host and just returns an “unable to authenticate” message without even asking for a password, add the following line to exim.conf:

  begin authenticators

  fixed_plain:
  driver = plaintext
  public_name = PLAIN
  server_condition = "${perl{checkuserpass}{$1}{$2}{$3}}"
  server_set_id = $2
>  server_prompts = :

This was a problem on CPanel Exim builds awhile ago, but they seem to have added this line to their current stock configuration.