I don't think it's a rule that JSON parsers are, in general, "pretty secure." Even if the parser itself is not vulnerable (to say, hitting recursion limits), how duplicate keys are handled between parsers has led to security vulnerabilities in the past for other things such as GET parameters. Or suppose an attacker gets a message through a few layers and that then causes a backend server to fail, like with the Swift errors he talks about, causing data loss.
But most other commonly uses transport formats are much worse, and much harder to parse. Start reading at http://search.cpan.org/~rurban/Cpanel-JSON-XS-4.02/XS.pm#RFC...