I read it differently. There's two ways to deal with trust:
1. you can try and hedge yourself against employees doing bad things. Like quitting for the competition or passing information. In this model, employees are paid mercenaries and none are crucial to the company. This is favored by corporations as it is good risk management.
2. you only hire people whose values align with yours, and where one strong shared value is sticking together.
The prisoner's dilemma is a good framework to see why either can work.
1. assumes defect/defect, which results in poor but positive outcomes. Corporations are inefficient, but they are profitable. You keep good people by paying them more than the competition, not by building trust and values-based friendship.
2. is cooperate/cooperate, which results in large positive outcomes for as long as you can maintain it, but the first breach of trust (the first instance or even possibility of a defect) results in a catastrophic negative outcome. For example, if you're having a few rough months and your CTO - who built 80% of the site and is the only one who understands the data model - leaves for a better paid job.
This is part of why it is so rare for more efficient upstarts to win against large corporations in their own market - by the time they get big enough, the startup looks too much like a corporation to maintain its cooperate/cooperate environment.
Where things get interesting is Andreesen's "Software Eating the World" essay. Some companies have recently surfaced (Instagram, Whatsapp, most hedge funds) where a small number of people highly trusting each other have managed to scale the outsize outcome to corporation levels.
And I think this is what Thiel is trying to say (or at least what he makes me think about): if your co-founders are practically "family", you might be more likely to go down that path. Whereas Zuckerberg prefers playing it safe, and assuming people will defect and scaling his company accordingly - especially since there is no shortage of capital to keep the best.