The Internet has never played nice with carefully crafted regulatory schemes. Since streaming became practical in the 1990s, a series of adventuresome dot-com entrepreneurs have been searching for a way to repeat the cable systems' original legal coup, bringing live TV to Joe User—preferably without paying to do so. (It's hard to make a living by streaming video when copyright owners can always turn around and grab back your profits by demanding higher licensing fees. Exhibit 1: Netflix. Exhibit B: Hulu.)
As you might expect, Cablevision's announcement of its planned RS-DVR (short for "remote storage DVR") drew the wrath of cable's traditional frenemies: the TV networks who supply most cable content. The networks were largely powerless against traditional DVRs, thanks to the Supreme Court's decision in the landmark Sony case. VCRs, the Court held, are legal to sell because customers could put them to "substantial noninfringing uses," such as "time-shifting" live TV for later viewing. Nor is home playback covered by copyright: that's a completely legal private performance unless you invite your neighbors over and charge admission.
The TV networks argued in vain that all of Cablevision's customers should be aggregated together as "the public," since they were all receiving the broadcast the networks sent to Cablevision. But the court concluded that the individual copies in the RS-DVR broke the "chain of transmissions" that took a TV show from broadcaster to viewers. The transmission from NBC to Cablevision's RS-DVR was a (public) performance; each transmission from an RS-DVR to its user was a separate (private) performance to an audience of one. The RS-DVR was legal.