Time Warner wants nothing to do with my (own purchased) cable modem beyond allowing me to use it. The vendor will only provide firmware patches to cable operators, and Time Warner won't touch my modem to help get the firmware upgraded.
All the cable modems I've used (UK) have always downloaded a an image over TFTP on boot. As I understand it they can come up with a very minimal loader and reach out for their config to the local "node" for configuration, and this can include new firmware. On the support line they're adamant that you reboot the things before proceeding past the IVR. Which makes sense.
The last I heard about it the different levels of service (bronze/silver/gold they were at the time, 5/10/20Mbit/s) are just based on the MAC the modem sends on this initial config/handshake. When I moved from 20 to 50 I was told to reboot the modem and it came up will an all new shiny more craptastic than ever web interface as well as setting it's WAN port to 50Mbit/s
With DOCSIS cable modems only the provider can update the firmware. And end user doesn't have the ability to update the firmware, even if they own the modem. That is part of the DOCSIS standard.