If you were that paranoid you wouldn't be using a web browser in the first place. After all, its some 3rd party software that has access to your passwords.

There seems to be a growing chatter on HN and elsewhere about how you can't trust free software because you didn't audit/write it yourself.

I'm not sure if people actually believe that or use it as a way to point out how they're smarter than other people.

Sure its possible that the free software contains something malicious, but such an attitude is not constructive. If you only used software you wrote yourself you might as well not use a computer. There are degrees of trust, balancing of risks, and free software has a much better reputation of not containing malicious code.