If you want any certainty, every free project is in need of auditing by the end user.
Nowhere did I argue that open source software is just as likely to have backdoors. It is, however, possible and ultimately your security still comes down to some 3rd party (my original point). Your argument seems to boil down to "software not audited by a trusted party is dangerous," but what you're saying is "proprietary software is dangerous." The two are not equivalent: there exist free projects which haven't been audited properly and proprietary projects that have. Calling lack of backdoors an inherent advantage of OSS creates a false sense of security and simply isn't true. At best being well-audited is an advantage of large and popular OSS projects, but even then it doesn't universally apply (e.g. OpenOffice) and there's no easy way to tell where it does.
(There is also the issue of accidentally introducing vulnerabilities, which your "many eyes" and "shame" factors don't necessarily preclude as evidenced by the Debian OpenSSL bug. Your original "proprietary software is dangerous" argument ignored this possibility.)