Me and her have very different theology point of views, however I believe we do know about anti-gravity.
Gravity is the least understood law of physics, we know basically nothing about it or how it works, we just have an arbitrarily observation of the phenomena of gravity. There has been much speculation with gravity, including Einstein's Theory of Relativity which defines gravity by describing our plane of existence being composed of a quilt of space and time. He could best describe it by taking a blanket and suspend it stretched out, and take a bowling ball and set it in the middle, notice how the quilt is bended around the object? If you roll the marble (a.k.a. the MOON) into the area of indention in the quilt, it will be pulled toward the bowling ball, and with a little inertia, you have an orbit. He proposed that any variety of mass exerts distortion in the quilt.
Its an interesting concept but you have to keep in mind is that it is all theory, much of we know is theory. For all we know we couldn't be anywhere close.
With alien technology, they already figured it out, we could take a huge leap in technology, but rather it is withheld. Maybe society isn't ready for a major revamp in their fragile reality, maybe we are.