The answer is yes and no; the stand alone tivo units have one tuner so you can only watch or record one thing at a time. But there is no reason you can't split the cable and go to the tivo and the tv. this may be too complicated for mom to be switching inputs but it gets the job done.
My wife wants to buy her mom and Tivo...any of these DVRs allow you to record one channel while watching another channel? This would be cable and not dish. Thanks for any suggestions. JD