In a lot of cases this is because there is more between you and the DHCP server than just a wire.
For example, I have verizon FIOS, I have an optical network terminal between my router and verizon. I know it isn't my ONT handing out a lease. At a guess, since I also have a 24hr lock on the MAC for a new IP (without doing an IP release first), my best guess is that the DHCP sever recognizes the MAC of the ONT that the DHCP request passes through. If there is an IP address reservation with that MAC attached already, it refuses to grant another one. IP release, wipes the entry on the DHCP table, so when a new request comes in, it is happy to grant one as there isn't one attached to that MAC address from the terminal.
On the cable side of things, probably something similar. They'll use the MAC of some device downstream to limit the reservation. Maybe your cable modem, maybe the switch port on the local node that only you are attached to, or coax to fiber bridge (since most cable these days is only coax from the curb, the rest is fiber from the curb to the ISP, though I am sure still plenty of all coax deployments out there), or something like that.