Having worked in data acquisition for several years, I'd say it would depend on a couple of things.
First, it depends on how the contract is worded. If there are no data deliverables explicitly spelled out in the contract, then the answer is no.
Second, only information that is normally a matter of public record would be required to be delivered. Internal documents that are prepared in the course of preparing the public records typically are not accessible by the public.
Third, is the outsource representing the FCC (i.e., doing their work) or are they providing a service to the FCC of corrdinating a specific project. If they are doing the former, then everything the FCC provides they must provide. The latter, we're back to number 1.