In particular, I could understand how two satellites connected by a cable would result in the cable being stretched. But I still find it hard to wrap my mind around the fact that we get a high tide where the Earth's gravity and the Moon's add (the far side of the Earth from the Moon), but we also get a high tide on the opposite side, where the Moon's gravitational pull is subtracted from the Earth's. The centrifugal force is (I think) a much better explanation. (I realize physicists don't consider that a force, but...)
So yes, tides really are weirder than I think.
(The other facts in the article were actually familiar, e.g. the fact that the tides in Hawaii are quite small, because it's not far from an amphidromic point.)