If the "fact" that the Moon has gravity is false, how do you explain tides? The slowing of the Earth's spin? Detections by ultra-sensitive gravity sensors? Peturbations of spacecraft?
Out of all the "facts" that could turn out to be wrong, the fact that the Moon is massive and has gravitational pull, is a near-certainty. Because, essentially, any other explanation is far, far less likely.
People often make comparisons between us, our ancestors thousands of years from now, and our descendants thousands of years in the future. But such comparisons do not work, most of the time; today we are in a position where we can learn, scientifically, much more than the people of the Roman Empire could for their time, and test it with far better accuracy as well. Sure, there are many things that we are unsure of in physics, but there are many other things that we are quite sure of; as sure of, as an early inhabitant of Europe was sure of the Sun shining in the day and the stars shining at night.
Simply put: when it comes to science, we're not morons.