It is semantics, yes. But given the dearth of people who have ever even heard of the copy flag, on the customer side or Cox's side, I feel like the precise terminology is important if the issue is going to get past Cox's customer service's response of "All of our channels have DRM and have for many years. That's why you have a cable card - to decrypt the channels." But decrypting channels isn't the problem, and hardly anyone at Cox will understand that. (And many customers won't either.) Throwing a term at them they've never heard of ("Copy Flag") might tip them off that they don't understand the issue like they thought they did and need to pass it off to someone who does know what the term means. It's a tactic I've used many times with first-tier tech support who is missing the point.
BTW, the reason your Hauppauge 2650 worked is because it used a cable card and you were using the Media Center software it came with, which was certified that it honored the Copy Flag. So it was able to record while maintaining the "copy once" DRM through to the recorded file. If you had been trying to use a third-party app or tried to export content from that app, it would also not have worked for channels with the copy flag set.
Like I said, my TiVo continues to work fine for recording, just like your Hauppauge. Its space-shifting features, though, where I can download video to watch on other devices, is completely disabled. I'll miss that if this is indeed intended and permanent.