Deliverability itself is a big industry and return path is the leader in the field. Mailchimp resells Return Path as it's "inbox checker" product which we use to analyze our emails to make sure we aren't tripping off spam filters.
The "Inbox Inspector" add-on shows screenshots of what your email looks like in a handful of email clients and runs what I'm guessing is a SpamAssassin check that returns a spamminess number. If this add-on is from ReturnPath, then the service they are providing isn't exactly "deliverability" once you've sent --- it's really a toolkit to inspect and QA your messages BEFORE you send them.
They also provide a whitelisting service (previously the "Bonded Sender" programme) which helps deliverability in a lot of cases, but the primary benefit is that it's pretty much the only way to guarantee delivery of large quantities of email to Hotmail.
So, they are closely involved with deliverability, but you're right in saying that it's down to Mailchimp to keep their sending IPs reputation clean.