That doesn't solve the original problem. It's just indirection from it... You still don't know what's going on in the background.
People don't trust Mozilla because they read the code, they trust Mozilla because they do exactly what was described above. They do the things that foster trust.
People trust Mozilla because someone could read the code (and probably, many people do).
People trust Apple and nobody else can read their code. This suggests open source is not necessary to build trust.
No, people choose comfort and projecting an image of status over privacy. It's not because they trust Apple.
I'm afraid Firefox is so abysmal noone could comprehend the whole project's code. Guess, we could only review a tiny bits of it (I had briefly read sync-related parts of code in hope I could replace them with something saner and simpler, but ditched the idea) and hope others did the same for other parts.
It doesn't solve the original problem as it is stated, but it still solves the original problem. 99.99999% of Firefox users will never look at its source code, they just trust the Mozilla brand.
It may not answer the technical question but it helps to resolve the human one, which is what their actual concern here is.
If some known person (open-source contributor or a startup founder) start using your product, ask for cross-promotion or endorsement of any kind.
Just be open. The more people know about you the more they are inclined to trust you.