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.