My organization does not use Z values and I should be able to disable them entirely. I have encountered more problems with tools failing because of a null Z value than not and we don't even utilize them.
edit: running Repair Geometry doesn't really help, as I could run it every single time I make an edit and still run into this problem. The fabric I'm working on passed Repair Geometry before attempting to use Copy Parcels, then Copy Parcels failed with a null Z value error.