The presumption that free software is sufficient or necessary to ensure all software you depend on is trustworthy is simultaneously naive and ignorant of what software is capable of. The only realistic way to develop trust in software is to trust the people who write it, and development processes associated with free software make that trust easier.
But merely being free software isn't sufficient - software developed in a way that prevents arbitrary observers from witnessing design conversations may still be free software, but doesn't give us a strong reason to trust the developers. We all know how easy it is to hide dubious code in the open. The libxz backdoor was discovered by examining the binary and tracking that back to the source, not through source examination.

@mjg59 💭 But didn't the libxz backdoor require the source available to figure out whether the behaviour was malice or just a quirk?

Since it's much easier to read intention from source metadata and source code itself, than from binaries.

@sheogorath Oh god no, bear in mind that the backdoor was embedding encrypted binary code into the library - it was actually initially easier to see that code in the binary than in the source