With a private blockchain network running on ethereum, do companies have to connect their internal systems to the network to participate?

I’m trying to understand more about how private enterprise blockchains work. I was just reading about JP Morgan’s liink network. How does this process work? How are companies onboarded and how do they participate? Like how could Bank A validate Bank B’s request on the network and how could it be trusted unless Bank B’s systems and data could verify it? How else could it happen instantaneously if Bank B’s systems weren’t integrated with the blockchain. Curious if anyone can give me an overview. Thanks!