I suppose it depends how the service is provided. Do CF actually act as an ISP, or reseller only? Perhaps the 3rd party services are just rebranded CF? Anyone know?

In the main (certainly for Zen) they are acting as a transparent Layer 2 service provider - much like Openreach do with their FTTP/TC network.

So as said you are not touching any CF Layer 3 infrastructure (routers, gateways or for that matter peering arrangements) this is all via your ISP (ie Zen) and their internet interconnects.