Very late replying, but that was the prevailing wisdom back then. My parents said the same thing, and when we got a dog, we went to the pet store because it was considered safer. These days, people will take in a stray to give it a better life, but that was not common in the 60s or 70s.
Also, you couldn't check for rabies without killing the dog, so it was not easy for a vet to just say everything was okay. The rabies treatment back then was expensive and included very, very painful shots, and the shots went on every day for a month. That's if you managed to catch it in time. If you were not educated for what to look for in rabies (and many people were not), you didn't know that someone's symptoms were due to rabies. Once the symptoms set in, no one survived. If a child was bitten and the stray ran away, the children were given the shots just in case, and it was agonizing for them. So rabies was a fear, and since strays could carry rabies, most parents kept their children away from them.
Things are different now, though. And in general, dogs live better lives now then they did back then. :)
I was charmed by the movie, but when I rewatched it as an adult I thought the part about the bitten uncle was the only realistic thing in the entire movie.