And that's what those 3 letters agencies do or at least should do. In addition of planting backdoors their job is also to make sure that their system are backdoor free.

In any case, the Microsoft is providing government with the source code of at least Windows (not sure about Office), so from a source code point of view, that is somewhat ok (minus finding people experienced enough to digest an enormous code base)

The main problem that is common with both Microsoft and OSS is actually checking the binaries. Except for China (to some extend), there is no government that is actually forking the project they use in order to create custom, controlled distro. So they are always going to have to trust their binary source. And that is the weak link.

When was the last time you reviewed the Linux kernel code looking for possible backdoors, found none and compiled your own kernel? Btw, when was the last time you reviewed the GCC code looking for possible backdoors, found none and built it from scratch? Btw, when was the last time...

Most companies and users get their pre-compiled distros and never bother because it's an impossible task so I don't see how open source is any better in this regard.