I have looked at many diagrams of the Chernobyl reactor and am wondering where the coolant comes from that enters the control rod channels when the control rods are raised. All the diagrams show coolant being pumped through the pipes that contain the fuel cells and then into the steam separators and back to the pumps (see enclosed diagram). All of the articles written about this reactor state that when the control rods are lowered, they displace coolant. None of the diagrams show additional coolant being pumped into the reactor vessel or being in any of the empty channels.
This is just a random guess, but have you considered there could be an expansion chamber? I had one in a house I owned, connected with its heating pipes (also a closed liquid system).
Expansion tank on Wikipedia.