Yes, their modems. On the connection that they provide for you.
A cable modem is considered CPE (customer premise equipment), meaning it is part of the infrastructure a telco uses to provide you with connectivity. Usually they own it, but in any case they have full control over it, as they should - it's part of their network. They may choose to delegate some configuration via a web GUI, but that's at their discretion -it's theirs to administer.
Business telecom has a formalized notion of a demarc (demarcation point), the place where the telco network ends and yours begins. AT&T owns and is responsible for the fiber/T1/POTS lines as they come through the wall, as well as the CPE (often a large rackmount Cisco router) to which it connects. Their contract is to provide connectivity on specific ethernet ports/fibre GBICs/whatever of that CPE. Whatever happens downstream of those ports is your problem, and whatever happens upstream is their problem.
Both sides will treat this connection as hostile - you'll have your own NATing router up and the telco's router, if it even has a configuration interface listening on your NIC, won't let you in. It would be inappropriate for AT&T to have any sort of access to the router you own and inappropriate for you to attempt any sort of access to AT&T's CPE.
Time Warner has been shifting recently towards placing WiFi on their side of the (logical) demarc. Which makes sense, since most people would rather not be responsible for administering any infrastructure - they just want Time Warner to deliver them WiFi. It sounds like you have this kind of setup, in which case Time Warner's access is not "backdoor" but "building owner" - you're renting a room.
If you'd prefer, you can (have them) turn off their WiFi, go buy a nice wireless router, and connect it to the modem. In this case Time Warner is providing you with a connection on an ethernet port; the device you've plugged in is your own (your side of the demarc) and they have no right to touch its configuration, nor are they responsible for it working correctly.
EDIT: The obvious analogy that would have simplified much of this is that a cable modem is like an electrical meter.