Timeshifting is not illegal, people do it every single day with TIVo etc... and court case says it is in fact legal.
http://en.wikipedia.org/wiki/Time_shifting
The legality of time-shifting programming in the United States was proven by a landmark court case of Universal Studios versus Sony Corporation (Sony v. Universal, or the "Betamax case"). In 1979, Universal sued Sony, claiming its timed recording capability amounted to "copyright infringement". Sony argued that the advent of its Betamax video recorder in 1976 did not violate the copyright of the owners of shows which the device recorded. A district court found that noncommercial home use recording was considered fair use and ruled in favor of Sony. In appeals, the United States Court of Appeals reversed this decision in 1981 giving the edge to Universal, but the Supreme Court of the United States reversed it yet again in 1984, and found in favor of Sony 5-4. The majority decision held that time shifting was a fair use, represented no substantial harm to the copyright holder, and would not contribute to a diminished marketplace for its product.
If timeshifting was illegal TIVo would be long gone.