Can I configure exim to accept mail on a server without an MX DNS record?

I'm trying to configure a domain that has never accepted mail from external sources to start. The server runs exim, which I've never used. I send a message to the domain using its ip, for example fred@123.456.789.012. exim logs: Quote:

rejected RCPT : The mail server could not deliver mail to fred@123.456.789.012. The account or domain may not exist, they may be blacklisted, or missing the proper dns entries.

Code:dig mx 123.456.789.012 returns NXDOMAIN . fred gets and sends mail locally (sends it to remote too), is not in the blacklist. Why does the message get to exim if the MX domain doesn't exist? Secondly, since it gets to exim, is it possible to get exim to ignore the lack of a DNS entry for the domain and send fred the message? I don't want to change the DNS record.