Right, if the government came out and said "yes there are aliens and they are visiting us" People would go into mass hysteria. There is a show on History channel called project blue book. Based on actual government case files.
I do think quite a few would accept this but how many would question our governments ability to protect our airspace? We’re pretty damn territorial by nature and we spend quite a bit to protect that territory. The same people crying for the government to provide them safety and security at any cost would be the same ones crying about how worthless the military is for not having the capabilities to keep alien craft from entering our airspace.
My guess is that if the government knows about anything of the sort then they keep it a secret because they don’t want people pointing the finger at them for something they have no control over.