Lyric discussion by Sir_Larrikin 

Cover art for Hovering Sombrero lyrics by They Might Be Giants

Well, my knee-jerk thought is that this about UFOs -- at least one photographed hoax was created by using a sombrero-like object.

Then, I think maybe they're simply calling the Sombrero a hat, because the human mind can't cope with it as a real alien-craft. And that they're saying that the aliens have been with us for many years --- waiting for us to evolve to a point where they can deal with us on their level. So, they're telling the aliens to just be patient, until we're able to communicate with them on their intellectual level.