im pretty sure that's the same time the alien movies got good...
Yup, they've noticed that the rash in alien attack/abduction movies pretty much perfectly predicts the rash in alien abduction stories. Before 1950 Hollywood rarely made alien stories and they were usually comic book-style stuff. Then starting in 1950 they were pumping out 5+ alien movies every year, many of which riffed off of the classic Kenneth Arnold "flying saucer" sighting of 1947. Over time the movies began to coalesce around certain themes and images, and, unsurprisingly, the alien abduction stories began to match just afterwards.
For example, while there were occasional rare claims of alien sightings before the 1960s (I'm talking actual alien beings as opposed to UFOs), their details were all over the place. These are the stories I can find before 1964 that describe the aliens themselves:
1897: H.G. Shaw claims he and his friend were harassed by three tall, slender humanoids covered in fine downy hair, but were able to fight them off
1897: Farmer in Missouri reports seeing alien that was "naked, golden hair down to her waist, most beautiful woman ever", flying a 20 foot long ship powered with 6 foot across propellers
1897: West Virginia man reports seeing eight Martians that were 11-12 feet tall and flew an illuminated craft with propellers
1951: Fred Reagan claimed his airplane was hit by a UFO, which was piloted by beings that looked like metallic stalks of asparagus
1953: George Adamski publishes a book claiming to have encountered nice-looking aliens with blond hair dressed in white robes.
Note - none of those previous stories involve anyone being abducted by the aliens.
In 1953, the film "Invaders from Mars" comes out. In it, aliens kidnap small-town Americans, do strange experiments on them, and implant mind-control devices in the back of their necks. Then in 1955, the film "This Island Earth" has aliens kidnapping American scientists in order to save their home planet.
Within a couple years, stories involving not just seeing aliens but being abducted by them suddenly appear, though the details are still all over the map:
1957: Antônio Vilas-Boas claimed he was seized by a 5' tall being with small blue eyes that communicated by barking. After being taken to the ship, he was forced to impregnant a very attractive naked humanoid alien that had a small pointed chin and blue catlike eyes, long platinum blonde hair on her head but bright red underarm and pubic hair.
1961: Barney Hill originally says he saw numerous humanoid aliens wearing glossy black uniforms and black caps that were "somehow not quite human", but doesn't say they abducted them. Months later, Betty Hill reported that the aliens abducted them and performed experiments. She describes them as short and nearly human-like with black hair, dark eyes, prominent noses, bluish lips, and grayish skin. They wore matching blue uniforms, with caps similar to those worn by military cadets, and were "not frightening" in appearance.
Neither of those stories were widely reported at the time. But the next three years continued to have many alien TV shows and movies, several with abduction themes, including these two TV episodes in particular: "Hocus Pocus and Frisby" from The Twilight Zone and "The Bellero Shield" from The Outer Limits
Notice they look nothing like the Betty/Barney Hill aliens or any others that had been reported by real people. They're not very human-like, they have no hair, they have virtually no noses, their lips aren't colored, they're not wearing caps, and their eyes are odd and far larger than in the previous stories.
On April 22, 1964, Barney Hill changed his story under hypnosis and now reported that the aliens who abducted them had "pear-shaped heads and large wrap-around eyes." That's the first time those features were mentioned, and they bear interesting similarities to the Outer Limits alien that had been televised just 12 days earlier.
The Betty and Barney Hill stories, which had been little known before then, first became widely publicized in 1965 and 1966, though front-page news stories, TV shows such as "To Tell the Truth", the first major book on alien abduction in 1966, then a major movie in 1975. Soon after that reports of aliens looking like "Grays" became commonplace, matching the 1964 Barney Hill description which seems to in many respects be a fanciful interpretation of the Outer Limits alien.