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[anagogy]

Well, based in studies and stories:

- The grey aliens are a negative/STS faction from Zeta Reticuli.
- Your main goal is to create a hybrid human/grey to cure a disease that plagues their species.
- Was reached an according between they and EUA and URSS. In exchange of technology the grays was authorized to abduze humans.
- They acting from lower astral plane and are behind all types of fundamentalism (as nazism, religious sectarism, materialism, etc.).

To kind of add to your points which are fundamentally valid to my understanding. Cliff notes for a very long story:

-The greys (whom are actually called the "Eloah") were created as a servant caste of another more powerful civilization hundreds of thousands of years ago that hailed from Sirius and Zeta Reticuli.
-They were designed to eventually die, by their designer alien gods (a gradually degrading genetic code), after a new less capable servant caste, that had less potential to overthrow them, was created (homo sapiens -- they wanted creatures smart enough to do menial tasks but not smart enough to do anything else) and they lack the ability to reproduce sexually (no genitalia/ability to produce sperm/ovum), hence the need to create a hybrid organism.
-They became self willed at some point (they were originally completely programmed creatures -- their progenitors were warned this might occur because they were extremely intelligent, and even programming eventually goes awry), and thus have sought survival of their race by incorporating a variety of organisms into their genetic code in order to extend their constantly decaying genetic pattern.
-Technology exchange with certain governments in order to leisurely engage in hybridization experiments (includes exchanges of genetic technology). Though keep in mind, we are getting their "junkers" which is fancy technology to our primitive reckonings.
-They promote service to self philosophy as per their nature (strong control weak).
-There are various dissident factions of them, some are malevolent, some are more friendly.
-They've lived under the earth in various caverns for hundreds of years (UV rays are harmful to them).
-There is a massive hive of them living underneath the Archuleta Mesa in New Mexico. The native Americans have legends of the "ant people" that live there.
-The confederation entities that met with Eisenhower offered to get rid of the greys (otherwise known as the cockroach infestation of the universe) but only if we got rid of all our nukes.
-Eisenhower refused, and thus negotiations with the greys began soon thereafter.