I had exactly the same issue as the OP - I was trying to work out why Exim was treating all local deliveries (ie messages generated by cron for example destined for a local mail box, or the output of 'echo "test" | mail ') as non-local.
Typical log entries from a command like:
echo "test" | mail userfoo
would look like:
2013-03-20 12:44:02 1UIIN7-0004t9-8R <= email@example.com H=localhost
(hostname.example.com) [127.0.0.1] P=esmtps
when they should simply look like:
2013-03-20 17:49:17 1UIN8X-0005iz-4Y <= firstname.lastname@example.org U=root P=local S=323
In my case the issue was with the way my mail wrapper was configured - on my OS - FreeBSD - you configure the mail wrapper in /etc/mail/mailer.conf, and I had neglected to change the various 'aliases' within that file to use Exim instead of the default sendmail binary. As a result I think the issuing of mail commands on the commandline meant the sendmail binary was being used instead of exim, resulting in a delivery attempt via ESMTP rather than local piped delivery.
Changing the mail wrapper config file /etc/mailer.conf from:
mailq /usr/local/sbin/exim -bp
had the desired effect of replacing sendmail as the default mailer binary for local deliveries. Bit of a school boy error really, I remember that being one of the first things I'd changed back when I first set up Exim 5-10yrs ago on FreeBSD, but since then haven't had any need to mess around with it!
Hope it helps someone anyway, this was about the only result that exactly covered my issue.
Replacing another MTA with Exim