The Wikipedia article has these relevant quotes from the court opinion:
The question is thus whether the Betamax is capable of commercially significant noninfringing uses ... one potential use of the Betamax plainly satisfies this standard, however it is understood: private, noncommercial time-shifting in the home.[7] [...] [W]hen one considers the nature of a televised copyrighted audiovisual work... and that time-shifting merely enables a viewer to see such a work which he had been invited to witness in its entirety free of charge, the fact... that the entire work is reproduced... does not have its ordinary effect of militating against a finding of fair use.[8]