They weren't 'taken' by it. It was likely to investigate it on the off chance it was possible. They had to try because if an enemy did and it turned out to be real, the advantages they would have would be huge. It's easy to look back from 2019 and roll our eyes, but I think the truth was less obvious then and it's likely our now easy dismissal of these things came from those very studies.
If you read some of the declassified documents regarding how they set up their experiments it's pretty clear that the studies were not being conducted in a scientifically sound way[1]. The CIA let the studies be performed with questionable methodology for a while, but eventually stopped funding the program. Then the DIA picked it up for a decade or two.
That's certainly a possibility. I believe they did something similar with UFO sightings by publicly giving them more credibility to mask testing of experimental aircraft's?
They did some research on "red mercury" and leaked plausible info on it, such that the other side would try it out, sink resources and get themselves killed (in the lab) in the process.
