I agree with your hypothesis but if you look at the History of the Apache people , they have long known of a subterranean species living amongst them as well as observed flying craft in the Dulce area.

According to what Phil Schneider had said, the US Govt. had it's first encounter with this underground species around the late 1800s while the Army was chasing fugitives into a New Mexican cave.
Also interesting as to how the Jicarilla Apache were coerced by the Govt. into accepting this specific area of New Mexico near Dulce as their reservation land.

One thing is certain and that is the Apache are well aware of and avoid these creatures at all costs and the results of the firefight between these Grays and high level US Security forces (with 66 killed in 1979) according to Schneider, is indicative as to why.

Also according to Phil Schneider, the Govt occupies the upper levels of these bases and the Grays the lower levels. Which would explain the disinformation campaign that might be used to conceal the existence of the base by the US Govt.

The fact that the Dulce base lies under sovereign Reservation land also adds to the base's concealment for it is illegal for US Citizens to trespass upon.