The trouble with all the conspiracy theories is that they have to explain all the secrecy if genuine non-humans are involved. I don't mean that of the US government, but of the non-human visiting intelligences. It they are real, something like this wouldn't be contained within the US but would be happening all over the world, and of course there are UFO sightings reported from everywhere. I can't imagine every nation would be able to keep secret any actual physical proof of visitors, and if the aliens were careless enough to lose one vessel with passengers and not retrieve it before it was captured, then this would happen elsewhere too given the amount of activity reported. On a degree of belief basis, it seems most likely to me that the whole affair is akin to the dragons and prodigies of the sky that were reported in ancient and medieval times and blends unusual events with mythology. Perish the thought that some leaders might exploit all this in order to have less friendly nations running off after red herrings and extraterrestrial Smaugs.
But there is intriguing evidence all the same, even if it isn't completely compelling. A possible reason for secrecy (by the aliens) is that they are time travellers and can only reveal themselves in our age to the extent that it was reported in their annals and is consistent with future history. Why be here at all? - probably because we are right in the middle of the Great Filter which will determine whether we survive to eventually move out into the galaxy, or whether we destroy ourselves. It could even be that they are here to protect us from their enemies who could be attempting to destroy them by destroying their past. Their reported form is generally rather close to human, and it's very unlikely that aliens unrelated to us would look anything like us, so these sightings are consistent with time travel. Perhaps it's their role to make sure we survive so that they can exist? Mind you, these time paradoxes are a bit boggling, so who knows? Anyway, it's a theory that explains their secrecy.
Another explanation, if they really are non-human visitors, is that they have very strict non-interference laws in primitive developing worlds. I don't really believe in this explanation, though, because there are just too many sightings and other reported close encounters to be consistent with it. If they have the technology to get here, and evade us as easily as they do, then they could easily evade any observation or encounter with us whatsoever. Quite honestly as well, if the galaxy is peopled by other intelligent folks then some of them would have been around a lot longer than we have. It seems to me that there would be traces of them all over the place if that were so - if not on earth then elsewhere in the Solar System, or observable through deep space astronomical techniques. Maybe the most advanced could leave no trace, but the developing civilisations out there would leave massive traces in their early days, as they move out beyond their own worlds.
Who knows? Personally, I rather like Ian Watson's explanation in his fantasy novel
Miracle Visitors