There were many tests of various flying (and mostly designed for spying) equipment in the 50-s and 60-s of last century (before good spying satellites were deployed). Tests were performed in low-populated areas of Nevada and New Mexico by DOD and DOE, and later some by NASA.
Some devices were seen by occasional observers flying. Their shape and pattern of flying was sometimes so unusual that some were interpreted by general public as alien's devices. Some devices were seen crashed.
Engineers from DOD and DOE (call them goverment officials)who recovered debrie in a rush did not want to speak much about the origin and the mission of aircraft (you may call it cover-up). Military personnel was not wery polite in using force to keep observers at a distance and even arresting some reporters trying to take close-up pictures.
Rumors, press, unaddressed calls to various goverment institutions made the frustrated public to firmly believe that there is something government knows about these "aliens" but does not want to discuss. Some people welcomed new business opportunities in selling to the public all kind of stories, pictures, souvenirs, t-shirts, etc.
But what would you expect in reality? A DOD press-conference like this:
"...This is the GX-5 non-pilot prototype aircraft designed to fly at the maximum altitude 34,000 feet over the areas of interest (say, Moscow). As you can see on our blueprints and photographs, it has aerodynamically smooth disk shape with dark anti-radar polimer coating on the bottom. It is equipped with 12" reflector scope, high resolution telecamera, and 120 ft of low-grain 35 mm infrared film for night shots. The effective resolution is 3 ft on the ground. There is also a high-resolution Geiger counter and a fast-neutron detector equipment on board. The propulsion system consists of 4 horizontal propellers mounted symmetrically in the holes in the aircraft disk body, the trust angle is adjustable in the range up to +/- 40 degrees from vertical to allow the aircraft to move with variable speed in any direction and to hover over the areas of specific interest. Each propeller is powered by 135 hp V-6 gasoline engine. Fuel tank has the capacity 120 gallons which is enough to keep the prototype in the air for up to 35 hours. Maximum horizontal speed is 170 mph, vertical 60 mph. The radio transmitter has 150 watt antenna power, operates at 140 MHz with noise-simulating phase modulation, and has the range up to 1500 miles. The reason that the aircraft crashed during the last test on Nov 2 in the area 51 was that the second stabilizing gyroscope failed at the altitude 23,000 ft..."
Do you expect something like this from DOD in the middle of cold war?