Is Randi becoming a geology denier now?

(Only kidding!)
I don't think there needs to be a net movement of mass vertically up or down towards the Earth's centre. At any latitude other than the equator, a sideways movement of a plate north or south (like a lot or earthquakes) would cause a net movement of matter nearer to or further away from the axis, causing the length of the day to change. Also, because this happens asymmetrically on only one side (Chile, in this case) it will redistribute the moment of inertia of the planet and shift the axis a bit.
I don't agree that we can't measure these changes. GPS relies on time measurements much more accurate than a microsecond, and by averaging several GPS readings you can locate a point on the ground to within a few millimetres. In fact, seismologists make measurements like this all the time in earthquake-prone areas to see whether the ground movement is speeding up or stalling.
(Recent BBC podcast about this
here)
I wonder whether GPS will now be recalibrated to take account of the new axis, or will we all have to accept that our latitude and longitude has just moved by 8cm?