I used to work for Time Warner as a Broadband Tech on the phones and in the field. If the equipment is not theirs, all they can do is activate and deactivate it. When they tell your account that you are only supposed to have such and such speeds that only works on their equipment which is designed to take commands from the Account system. A third party device can only be allowed to work or not as far as I know. Its been a few years but my father in law pays for the basic speeds and with this modem he is getting the max speeds possible for our area. My father in law bought this modem from Amazon instead of renting. His speeds are triple what his TWC account services are supposed to be. Probably because TWC can't regulate the speeds on it with their account system. 
Amazon link:

  • Great for the occasional Internet user. A good choice for checking email and doing a light amount of web surfing — at a budget-friendly price.
  • FREE shipping if you qualify for a self-install Easy Connect Kit

$ 14 99per month
Time Warner site link:
https://www.timewarnercable.com/en/plans-packages/internet/internet-service-plans.html

Buy your own modem