We only have one. This is the first one we've done.I would say that that is the root of your evil. You aren't watching a recorded show you are watching the show on demand.
From what I have read Tivo's have onboard recording, about 1000 hours of SD or 150 hours of HD. Maybe it is time to clear some of the older recordings.
And I think it is ALL On Demand. I learned that TiVo has something they call a Smartbox. That's kind of what it does - provides on demand.
I did however look at my bill - it does say DVR. I'm even on some kind of promotional discount for it, otherwise it would cost a lot.