That's the opposite of how it works. The Senior Council can take up matters if three of them vote to. The Athenian assembly and council were both subject to the public courts.
I never said it's a liberal democracy. As best I can tell, checks and balances is an outgrowth of separation of powers that first developed in 1787.
Read Polybius about the Roman republic. He thought that that state had the ideal balance between democracy and aristocracy. Something for the senate and something for the plebs. I think he would have classified the council as some form of aristocracy, the power of the senior council is just too big and the demos has little influence. But maybe a meritocracy?
What is important for being a democracy is where the real power is. Is it with the people via their representatives or is it with a small nobility that is selected not because the people have spoken but because of their wealth, status and family. The old boys network.
In the council the real power is with the senior council. Both theoretically but more important practically.
So if for example the ability to buy and steal elections and politicians becomes too great and elections are more and more a formality you would live not in a democracy but a plutocracy or if one person steals all elections an autocracy.
The 500 were chosen not by ballot but randomly from the different tribes. Some of the ancients thought that even better than election but if done correctly it might introduce some idiots but we have them now as well.
It also makes it less of an aristocracy. The 500 are still seen as the representatives of the people. It was seen as a form of election.