actually, the US government is the one supporting the UFO stories. they're developing new aircraft all the time, and they don't want other governments finding out what they have, otherwise they'll try and steal the technology.
anyway, billions of light years is a gross understatement. there's trillions of galaxies out there.
and the distance between the galaxies just keeps getting bigger.
the further away from us a galaxy is, the faster it's going. and the furthest the hubble can see is about 13.7 billion lightyears.
the reason it can't see further is because at that point, objects are travelling faster than the speed of light relative to us; so the light can't reach us.
Einstein's relativity does show that objects can't move faster than light, otherwise their mass would become infinite - M = M0 x 1 / SQRT(1 - V²/C²) - and the time they would experience would be zero - t = t0 x SQRT(1 - V²/C²)
but that is assuming space is static (no distortions in space)
in fact, what they've found is that space itself is expanding.
think of a balloon, with space being the surface of the balloon.
it's the same as that, but with 3 dimensions.
although the galaxies may be travelling at a much lower speed relative to us relative to static space, the actual space distortion is very significant given the billions of lightyears that's stretching between us.