Some say that an mail server can deliver email to the IP address where the domain is pointed to by A record even if the domain does not have corresponding MX records, though it is not recommended.
However, from my experience, the email will not be delivered on the shared server without MX records at all.
So, why won't it be delivered?
Is it connected with the shared IP address or is the email rejected by spam filters as the domain does not have proper records?