That's total bullshit.
Democracy runs on the equal application of the rule of law.
Of course, no democracy is perfect. The degree of imperfection can be measured in how much they run on the honor system...
And how exactly do we maintain equal application of the rule of law? We put honorable people in the position of applying the law. The honor system.
Transparency and constant monitoring.
To understand how to run an organization without trust, think like a capitalist.
Does a bank function because of honesty?
No, everyone is watching everyone else, all the time.