I get the feeling however they may be talking about modems that you get from Cox
Are you referring to this line in the first link: "If you did not purchase your modem new from a third-party retailer but instead purchased or received it in used condition...?"
Cox is just referring to lost or stolen modems. There may be either a blacklist via MAC or a conflict with a servicing address. If it's used and won't register, just call Cox to research why.
You can purchase whatever DOCSIS you want from anywhere...just as long as its make & model is approved and not reported as lost, stolen or conflicted.
Normally when you purchase from a Cox Store, the rep (sometimes) should register your account for a "self-install" and when you get home, connect it and wait...it should register.
However, if you purchase from somewhere else, you won't get registered for a self-install. In this case, just connect, call Cox and navigate to whatever option to register a new device. This will lead you to a techie somewhere around the country...and not a sales rep (yuck!).
I have landline service with Cox so the rep freely loaned me a combo DOCSIS-landline modem.
After 6 months, the DOCSIS portion of the combo device failed. I still had my previous DOCSIS 3.0...which had previously registered fine with Cox...but when I reconnected it the second time, I still had to call to register and activate it.
Bottom line: If you're not registered (scheduled) for a self-install, you'll need to call.