I think we have to be careful. His belief that the Earth has been visited by aliens has to stay separate from the 1951 episode event. (Sometimes referred to as 1958, by the way).
There is a possibility that what they saw was terrestrial. In the clip he said he looked at the developed film and saw that it was clear and correctly processed, but did not run the film and view it.
Did the camera crew see something? The film would prove "yes" if found. Did they accurately describe what they saw? Cooper would have no way to confirm that.
Cooper also confirms he saw lenticular or saucer shaped objects by the scores, as did his fellow pilots. He said that these objects exhibited technology beyond that of anything he knew.
Cooper personally saw a number of esoteric objects in his career.
Cooper believed there was evidence somewhere that aliens have visited us.
I don't think you can make a leap and say that what Cooper saw at any given time was alien, though there may be a possibility it was. I do not know if he ever declared that anything he ever saw was proof of aliens. I listened and read about 5 different interviews today, and if you listen carefully, I don't think I heard him once explicitly connect what he saw with proof of aliens. He seemed slightly less clear on this the older he got, though.
As to the crew, who if they served in the military we should respect. However, we only know what Cooper said he remembered about this, and do not have the film or descriptions of what they saw. They may have seen a new military aircraft - certainly there were many new classified prototypes at this time. If they did see an alien ship, even the film could not prove this, but only imply or infer. I see nothing where they "lied" about it.
Back to your original question, as humans living in the 1950's, the film crew certainly were exposed to science fiction films, SciFi magazines, and flying saucer lore, which could have colored their interpretations of what they filmed.
In the 1930s and through the late 1940's, there was still mythology that Mars could be inhabited, and there was absolutely no proof that planets existed outside of the "9" we knew about.
In the late 1950's, better astronomical equipment began to erode the idea that Mars might have life, and some astrophysics models suspected that the creation of stars allowed for planetary formation by disc accretion. This is why Forbidden Planet (1956) is so radically different from George Pal's War of the Worlds film.
The original screenplay (1952) was called Fatal Planet
and set on Mercury. By early 1956, Cyril Hume realized the back story had to be completely altered. War of the Worlds (1953) had more restrictions since it was Wells classic, but in 1953, the Martian theory was still allowable.
I think one of the death knells was the blunder by the National Geographic Society in September 1955. As Mars came close, they stated, "The sudden appearance of a large dark spot on the surface of the planet Mars was announced yesterday by the National Geographic Society in Washington. It was also claimed that this discovery supported the conclusion 'that Mars is not a dead world, that the darkening is due to the growth of plant life.'
" They were taken to task by the scientific community for this statement.