If you read the blog post in the OP, you will see that CMC is saying they don’t believe the leaked information came from CMC. They are saying they believe that someone used a list of email/password combinations leaked from other sites, and used these combinations to try to login. When logins were successful, the hacker knew that the email was associated with an account at CMC.
At some point, they did put special care in the wording to state that:
The "our own servers" seems like a deliberate careful choice of words, to cast a shadow on any third-party provider that has access to the information for, let’s say, marketing purposes (see https://coinmarketcap.com/privacy/). This would also play along with there being no passwords in the leak.
Given that CMC accounts really don't contain much valuable information, it might not be unreasonable to think they are not employing sophisticated detection systems to try to detect unauthorized logins. I would presume that someone logging into 3.1 million accounts would not do so from a single IP address, and a project of this scale would likely have been done over time, and using many IP addresses.
CMC claims to "reach" hundreds of millions of users every year, so 3.1 million email addresses would likely be a small subset of all the email addresses in their database.
They also probably want to be careful to not acknowledge the email list is valid. Doing so would implicitly acknowledge that any email address on the list is an email address associated with a CMC account.