If a DNS lookup returns no MX records why doesn Exim just bin the message?
A0312: If a DNS lookup returns no MXs, Exim looks for an A record, in accordance with the rules that are defined in the RFCs. If you want to break the rules, you can set mx_domains in the lookuphost router, but you will cut yourself off from those sites (and there still seem to be plenty) who do not set up MX records.