I think the excerpt needs to be taken in the context of the previous paragraph and book 6 in general. Book 6 deals with the fundamental notions and foundations of democracy. In section II, there are two primary principles of democracy, that in one instance, democracy and its principles should be observed (like equality, majority rule, etc.). The second is that there be true autonomy for a citizen.
In the section you quote from (AP, 6, II,P2), the issue in question is the position of the electorate and appointments to office. This is in essence term limitations, surety of integrity in office, etc. From this point it gets to where your question is;
"Of all magistracies, a council is the most democratic when there is not the means of paying all the citizens, but when they are paid even this is robbed of its power; for the people then draw all cases to themselves, as I said in the previous discussion."
In the early fifth century, Solon becomes the head Archon (of the three) in Athens (following Drakon some time before). He introduces a series of reforms in the wake of the Damasias affair (of which there is very little information about, but this helps to date the timeframe in which the Solonic reforms are established, which is around the 580's). Among the various reforms Solon imposes, such as the end of the seisaktheia
(shaking off of burdens) imposed on destitute citizen farmers (Gorgoi