It does seem the one that is product attribute that is system does not want to be in the layer.

I will look into it now. Having said that, one would think it might be worth creating a new product attribute identical to the no system one and then 'do assign your data to the new attribute and refresh index..'

that should be a quick win, if you want to do this and you miss a script to update the attribute, I surely can provide you with this script