How?

I understand how blockchains can be used to trace the history of transactions back to the root but I don't see how that can be used to do secure key distribution.

Assuming everyone trusts the root block, how does that trust get transmitted down to subsequent blocks?

Read the links in the post and the website. Here's one of them that directly answers your question:

http://www.aaronsw.com/weblog/squarezooko

Every time I read an article by Swartz I feel our community' lost all over again. :-(