MAC address locked on broadband modems?

Has anybody else out there noticed their broadband provider locking the cable modem for one device? And, how are they doing this? Is it MAC address locked?

DHCP /release + /renew only works for the last device connected to it at the time of a Charter initiated reset. I vaguely remember somebody mentioning a similar issue with Bellsouth/AT&T DSL modems.

Backstory:
Noticed this when changing the broadband router... ONLY the old router would renew DHCP from modem. All other devices wouldn't. Called tech support and went through the typical only one computer connect and they initiated a modem reset. After that, ONLY THAT COMPUTER would DHCP renew from modem. Everything else wouldn't.

Call back and mention the strange behavior. They immediately try to upsell me a "home networking" for multiple computer usage plan and state that "using multiple devices is not supported". Hmmm... very suspicious. I refuse "upgrade".

So basically, the only option is to bold faced lie to tech to get them to initiate a reset while the router is connected to the modem. Low-and-behold everything is suddenly working just fine.

Some quick testing once again verified only THAT device would new DHCP renew.

Yep, rebooted every time. Didn't seem to fix. However, didn't try the special "reset" button on the broadband router... that might do the same thing the customer rep does...