Okay, clarification about some aspects of international space law.
Article VIII
A State Party to the Treaty on whose registry an object launched into outer
space is carried shall retain jurisdiction and control over such object, and over
any personnel thereof, while in outer space or on a celestial body. Ownership of
objects launched into outer space, including objects landed or constructed on a
celestial body, and of their component parts, is not affected by their presence in
outer space or on a celestial body or by their return to the Earth. Such objects or
component parts found beyond the limits of the State Party to the Treaty on
whose registry they are carried shall be returned to that State Party, which shall,
upon request, furnish identifying data prior to their return.
(Treaty on Principles Governing the Activities of States in the Exploration and Use of Outer Space, including the Moon and Other Celestial Bodies, 1966)
So if United States came into possession of, say, a wreckage of foreign military satellite, then according to the Treaty, United States must return it to the rightful owner. Of course, US military & intelligence did not want to do it, since such wreckage is a valuable source of intelligence.
So how to avoid such burden? Simple - to classify such things as "unidentified". If USA aren't sure what it is, then USA have no legal obligation to return it... right? So instead of
"wreckage of Chinese military satellite" (that they are obliged to return), they just wrote
"crashed unidentified spacecraft" (that US have no obligation to return).
And so we have a lot of secret - highly secret! - documents, talking about "unidentified spacecraft". At some point, someone not involved get a view on documents, and made obvious (wrong) assumption: that they are talking about alien spacecraft! And the "story" became public.