You don't need an integration at all: you just call the other company smart contract to see if the user has a specific type of equipment defined by an NFT.

Problem is that this information should be private.

If I know you are a heavy user of some other game, maybe I can sell you something to advance in the game quickly instead of having to play a lot.

Is it desirable? For a game company, maybe. But for an insurance firm?

I am not so sure.