The corp website and wiki say their retail locations are 100% company owned.
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http://www.chick-fil-a.com/Company/Careers-Franchise-Opportunity
What corporate site were you looking at? This one certainly suggests that it is a franchise deal.
It’s not a regular franchise like the other competitors.
They (CFA Corporate) owns the business, the real estate, etc, you are called a “franchise” but basically an employee. To get the “franchise” you are prevented from having any other active business ventures, also.
Nothing wrong with that, it just wouldn’t be as profitable for the “franchisee”. They are a successful and ethical operation.