So I contacted Anveo and they said their provider, which is bandwidth.com, seems to be passing CID for free right now, so that's why we've suddenly noticed CID info being shown even though it isn't enabled in FreePBX (nor is the paid lookup option on Anveo selected).
They told me the number also does not have a cnam entry, so they told me how to add one for $5 through their API. I went ahead and did it with a different DID as a test, but the free lookups out there aren't showing anything yet. We'll just have to wait and see I guess...