"TiVo Faces Off With Flattering Clones" is the tale of the classic battle of a company trying to maintain their branding and keep from becoming part of the lexicon. Xerox fought it tooth and nail (and lost miserably), Adobe is currently fighting the term "photoshopped" (and losing), I hear people call almost any personal mp3 player an iPod, and now it's TiVo's turn.
I had this happen to me last summer, when a Comcast cable installer came by and mentioned that they'd be offering TiVo in a few months. When I pressed him for more info, it turned out to be a generic DVR. It's not hard to hear people say they "Tivo'd that program" in interviews these days, though few of them actually own a TiVo instead of the DVRs many companies offer.
In the long run I don't think this will be bad for the company. They built a device that provided a fundamental shift in how we use a TV and they have attained the status of becoming a unique new word in our collective vocabulary as a result. I know that millions of people saying the word TiVo doesn't equate 1-to-1 with new customers and the company considers it brand confusion, but it certainly can't hurt if your brand and product recognition get to be so good that people use it as a term for the functionality. Everyone knows that to "TiVo" something you tape it on a hard drive based recorder. When they go into a shop looking to buy one, they'll only know one term to describe it, and that could equate to long term sales for the company, not confusion.