Yes, in theory it is possible. However even 100% secure proprietary software must be assumed to be insecure, because we're still running on blind faith, which is patently stupid for anyone who requires security.
You run OpenBSD, don't you? (To be fair, their approach since the 90s seems a lot more reasonable now)
No, my views are not based on my own needs or paranoia. As a security-oriented software developer I recognize that software that claims to be secure needs to deliver, because people like Snowden, Assange et al. may be relying on it some day.