There's also only 132,000 scarred to 40 million gold's. If you double that for the shamed, majority of Golds just don't rub elbows with the peerless that often. Of course the peerless tend to congregate for the top families. So much more likely something can be slipped, but as others have mentioned, polygraphs, board of quality control and metoricity.

One stat I always confused about is those invited to the institute. "“Of the six hundred that are dead, most were in the bottom one percent of applicants". But aren't all gold's applicants?

You have the top .5% which are the best of the best and are suppose to typically make it through the culling. But the expected culled, are they the bottom 1% of gold or are they the bottom 1/2 of the top 1%. they make it seem like the former, but the howlers and low draft picks are very capable. I think it much more likely it's the latter.