If the private repo had the MIT license in it, then it was licensed with the MIT license, regardless of how widely or publicly the repo was distributed.
It isn't that clear-cut. A license is a legal grant of rights from the copyright holder to the licensee. A license file is just documentation. A repo can have different parts that are covered by difference licenses and there are different ways to mark the licenses, whether in the text of each file itself, or other top-level files that document the status. It is also fine for internal working copies to not have all their licensing documentation perfectly applied the instant a file is created. In particular, in many companies, individual software developers don't have authority to license software on behalf of the company who owns the copyright, and so any markings they place in the repo are just tentative drafts pending legal review. So in the context of a private working copy, the existence of a license file doesn't have a ton of legal weight. What matters is when the copyright holder chooses to grant a license, via whomever the company gives authority to do so.
Once the organization publishes the software to others, whatever license documentation they include with it is binding, unless other issues trump that (like them not holding the copyright to begin with).
Ok, it's not true in the general case, but it's true in this specific case. The project was intended to be an open source project from the beginning; we were intending to open source everything.