Earlier quoted context omitted.
Spectrum remote manages your hardware even if you bring your own modem. This nearly entirely consists of deploying firmware updates once a decade, but they can also command other things like modem reboots.
If it's your own hardware, what's stopping you from closing the port they connect to?
AFAIK, they can/will kick you off the network if your modem is running unverified firmware. I think this is a regulatory requirement, but don't take my word for it. They don't want anyone to have free access to the network, you could do things like spoof your MAC address to get free service. I'm sure you could also do something much more malicious like crash parts of the network.