Alright, but now you trust that person. Which might be fine, but as an exercise in paranoia is not the greatest answer. As a social proof, somewhat better - create the opportunity for many people to examine, and at least some of them will find things and talk about it. Now the trust is in the shape of the general mass of reviewers - that it contains people who will review the code and reveal their findings.
In a word: no. With open source code, you could use software authored by the NSA, like SELinux, or you could even hire a manifestly untrustworthy party like Hacking Team to author some code and still be able to trust the code.
In Apple's case, there is a fairly good reason to trust Apple because it would be a hell of a kabuki theatre production to have the FBI and Apple battle in a Supreme Court case while colluding in secret. But would you trust a defense contractor? A telco? Limit or ideally eliminate the need for trust. Fortunately it is possible to reduce the need for trust below having to trust groups or individuals.
Isn't that discredited by Apple's "goto fail" bug? A critical function was mistakenly circumvented in an extremely transparent way, and yet the source code sat on their website for a long time without anybody noticing. Nobody even ran coverity on it.
