Let me use another analogy. Take a steel bar that's 18" long and grab it firmly in your hand 6" from the bottom. Using a mallet, tap the bar to make it ring - it will vibrate for a very short time because the vibrational impedance of your hand is much smaller than that of the bar so the vibrations are transferred to your hand which has high internal damping.
Now embed those 6" into a big block of concrete and give the bar a tap. You'll see that not only has the resonant frequency changed, it will ring for a very long time. This is because the impedance of the concrete block is much higher than that of the bar so the vibrations will tend to "stay" in the bar and dissipate only due to the damping of the bar itself. This in spite of the fact that concrete has a very high coefficient of internal damping.
The rigidity of the machine is fixed unless you want to start replacing structure with e.g. steel. The key is to match the table to the rest of the machine.
If you look at something like a bridgeport or Haas or whatever, everything on the thing is more massive and more rigid. What works in one case won't necessarily be best for the other.
If you rigidly fix a machine like the Xzero to a very rigid and very massive table, any vibrations in the machine will tend to not transfer to the table due to the impedance mismatch and will dissipate entirely in the machine. A table with similar or less mass and rigidity will tend to absorb and dissipate vibrations from the machine. I personally like the idea of George's table with legs filled with sand. Sand has very high internal damping.