You and I were coming at this from different angles. I was kind of under the impression that you were suggesting that said QBs were unwanted and only got their positions because of networking, from this quote (which I probably mis-interpreted)

Think about how many personnel moves and coaching moves happen because of networking. Don't have to tell you how many star players were unwanted at some point in their careers, you can start with 12-13 starting QBs in the league right now.
Yeah, you can certainly find QBs from the scrap heap, but outside of Brady and perhaps Fitzpatrick and a couple others, I question how many of those QBs are stars.