Were those six emails spam or legit email? Spammers use a variety of tricks including mining DNS records. For example, some spammers will send email to lower priority MX records rather than honoring the higher priority ones. A spammer might be sending emails to A records in the hopes that perhaps, just perhaps, there's an email server running on it that will accept the email or contribute to backscatter spam. If it was spam, then don't worry about it.
If it was not spam, then you'll need to check the possibility that there's a misconfigured DNS server out there that is not refreshing its DNS records. Those 6 emails that were sent to the wrong email server, were they all from the same domain? If so, see if you can find what DNS servers that domain is using (for example, if it was a single company, their corporate DNS servers are likely misconfigured. If it was from a single ISP, see if you can work with that ISP to check their DNS servers that they have their clients use).
EDIT: So those six emails were not all from the same domain. Do all emails from those six domains hit the wrong email server or just some? Perhaps each of those domains' DNS servers are flawed in their configurations. Six domains out of the hundreds or thousands that send email to that customer of yours is still small I suppose. In my opinion, most DNS servers are intentionally misconfigured for "performance" reasons, especially for TTL values. Use dig or nslookup, select that domain's DNS servers to query against (if you can find them; shouldn't be too hard) and then look for the MX records for the domain that received the emails at the wrong email server.
Domain being sent to: LeeQuarellaCustomer.com
Domain of one of the emails that was sent to the wrong server: ErrantSender.com
DNS Server of the sender: 10.0.0.1
nslookup server 10.0.0.1