[exim] Mail never leaves domain

I have exim installed on a box essentially just for sendmail
capabilities. it's hostname is foo.com and I'm trying to sendmail to
user@???, but it never leaves the box, since exim thinks it's
authoritative, whereas our mail server is actually located elsewhere
(mail.foo.com). what do I need to do to have exim forward mail for
user@??? externally?

using the exim4 binary directly works fine, btw, except when sending
to any user @foo.com

here's my initial update-exim4.conf.conf:

dc_eximconfig_configtype='internet'
dc_other_hostnames='my-nifty-host'
dc_local_interfaces='127.0.0.1'
dc_readhost=''
dc_relay_domains=''
dc_minimaldns='false'
dc_relay_nets=''
dc_smarthost=''
CFILEMODE='644'
dc_use_split_config='true'
dc_hide_mailname=''
dc_mailname_in_oh='true'

and the alternate config using a smarthost and got the same result.

dc_eximconfig_configtype='smarthost'
dc_other_hostnames='my-nifty-host'
dc_local_interfaces='127.0.0.1'
dc_readhost=''
dc_relay_domains=''
dc_minimaldns='false'
dc_relay_nets=''
dc_smarthost='mail.foo.com'
CFILEMODE='644'
dc_use_split_config='true'
dc_hide_mailname='false'
dc_mailname_in_oh='true'

Any advice? I'm sure I'm missing something basic.

Thanks In Advance,
Stephen