Alan Smith and others have always measured zero voltage by doing so, as for example reported earlier. This should rule out the LEC being an electrophorus.
Only a small number of materials have been tried so far. The question arose about the behaviour of one material - which exhibited an uncharacteristic effect when placed on one side of a glass slide, with a counter electrode on the other. This is important - as "the exception proves the rule".
Hopefully, in time we may find other materials that behave in uncharacteristic ways - which will all help in building a more useful model of what is happening.
Note that the illustration was not being used to say that the WE is an electrophorus - it was there to show that if you dangle a lump of something, that is charged, and you measure its potential to earth (and yes, you would need a high impedance meter) then you would see a voltage. You just seemed to be struggling with this concept.