There are two main tanks in the stage, the top ~half is liquid oxygen, and the bottom ~half is kerosene. The liquid oxygen is lighter, and boils off pretty quickly once they open up the vents. So what little fuel is left (the kerosene in the bottom tank) also settles to the bottom, which helps push the CoM even lower.
For the vertical landing, this would seem to work against them, but I guess the mostly empty tanks don't dominate the considerations. Falcon has oxidizer on top in the conventional manner, as far as I know (they mention LOX feed lines going through the fuel tank).
[1] The N1 rocket had oxidizer below the fuel in every stage, apparently because they wished to use spherical tanks, and this allowed packing them in a conical shape - the oxidizer tanks are much larger.
It is however true that they can vent it pretty quickly though, leaving the only remaining propellant in the bottom tank.
Actually, an inverted pendulum -- where most of the weight is on the top -- is easiest to balance on top of the rocket thrust. Coming down at high speed, this would be aerodynamically unstable, but this is why they have the grid fins, to move the center of aerodynamic pressure behind the center of gravity.
Also, after the landing they vent the remaining oxygen, and afterwards people come aboard to weld the rocket legs to the surface so it wouldn't slide off.
Maybe very strong winds would be an issue, or very rough seas immediately after landing but they wouldn't launch in rough weather anyway.
After watching the video I don't know what Musk is talking about. Maybe he's talking about a maximum double amplitude.