Is absolute electric potential arbitrary?
As discussed in your previous question there isn't any point worrying about this. You can't run a wire to infinity to measure the potential with respect to that. 

Pretty much everything you will be working on will require that you connect the black lead of your meter or the ground clip of the scope to some reference point that is within reach. The closest thing to true ground potential you will get is the planet Earth but even this has variations due to the sometimes surprisingly poor conductivity of the earth in some locations.