Of course we can keep secrets from the Axis Point.
I'm trying to point out something different; we don't have a contingency plan. What if one of us is compromised? After the subsequent interrogation, the dragons will know locations and codes for every single piece of the subnet. That's bad enough. At worst, they close off our communications network entirely, locate each of our respective sources, and exterminate the Gospels forever.
We aren't as compartmentalized as you think, Prophet. If we lose even a single member, whether through Axis Point probing or simple betrayal, we might lose our only means of unity and we might all get shot. Just putting it out there.