Certainly not. It was more common for theaters to play classic movies back then. Additionally, classic movies were excellent material for television stations to play and were one of the big draws of early cable television. Indeed, the television broadcast rights for motion films became a major source of revenue for production studios. In some respects, prior to the modern age of content on demand it was much more likely for people to be exposed to popular movies on television.

Some examples. NBC had "Saturday Night at the Movies" which ran from 1961, and CBS had the "CBS Thursday Night Movie" which ran from 1965 through 1975. And, of course, you have cable television channels like HBO starting in 1972 and Showtime starting in 1976, before VCRs were widespread. And you have various local channels.

Interestingly, because "top tier" films could still earn money at the box office years after release and their broadcast rights were very expensive the movies that tended to get the most airtime were often "lower tier" films. Which ironically meant that many of those lower tier films ended up being watched by far more people than saw some of the best and biggest films of the day or of the recent past. Though many films that were very popular in the theater were also very popular on television. For example, in 1976 NBC paid $5 million ($22 million in today's dollars) to air Gone With the Wind just once, but doing so broke ratings records. To pick another film, The Wizard of Oz was typically broadcast only once a year until the late '90s (by different broadcasters but mostly by CBS). It became something of a national event that many families would come together to watch.

How each film from the past fared after its initial release varied wildly. Some movies, like Casablanca (incidentally the most heavily shown film on television prior to the VHS age) or The Wizard of Oz, deepened their initial popularity through later showings in theaters and on broadcast television, becoming well worn parts of popular culture. Other films gained what might be fairly said to be a degree of "unearned" popularity due to the needs of television stations to fill their schedules with material. While other films suffered an unwarranted diminution of attention as they faded from the box office but weren't sufficiently broadcast television friendly to live on as an irregular companion of everyone's lives right in their home.

More of course can be said, but /u/lord_mayor_of_reddit wrote this answer which might be of interest for you.