That's a great question. Seems like the data itself is under an open license but the company charges for API access to it, presumably for the effort they've gone to consolidate the data and for running the API service. See the legal info https://opencorporates.com/legal/licence and in particular the "The OpenCorporates database" section of the page.
The OpenCorporates database is licensed under the Open Database
License. A plain language summary of the ODbL is available on the Open
Data Commons website.
We source the information in our databases from government and other
sources through a variety of means including: directly from government
websites and APIs, from publicly available datasets, or through
Freedom of Information requests. We spend a lot of time, effort, and
even money in getting this data and turning it into a workable and
highly usable resource.
We do not claim any rights over the information we receive from our
government sources, and attribute them whenever possible. This is
known as the "Contents" in the ODbL license.
We do however claim rights over our database of this information.
What's interesting in that document is that there is mention of free API access in addition to paid access but I could not find any additional information access.
We offer free access to our website and API, and also paid-for access
to our API. If you have agreed to a paid-for contract for use of the
API, these terms and conditions supplement that contract and, in cases
of conflict, the wording of the paid-for contract will take
precedence.
I welcome edits to expand this answer and hope someone else can also give a better explanation.