Anonymous doesn't mean secret. If the governor of Ohio says his people want Trump over Hilary, just trust him, you don't need to know how he knows would you? I mean, I don't trust unauditable electronic voting machines. I certainly wouldn't trust someone who couldn't even point to the machine he got his info from.
Much of the voting system is an exercise of trust. The most reliable part of it, besides the fact that election officers are publicly known and accountable, is that officers from both parties oversee each voting center. Your trust is that the adversarial nature of the political parties will raise alarms if the ballots are tampered with.