Taking Apple's word for their browser being secure and other browsers not is just as if not even more ridiculous.
What fair, independent way of determining browser security would you suggest be used instead of an audit?
While that's just Safari and Chrome, that's probably ok. But what happens when it's Safari, Chrome, Firefox, Opera, Brave, etc, etc?
For the security test, there are various ways that an org builds software with integrity, and it's the sort of thing that requires a huge amount of effort to get right. Standards like FedRAMP, SOC2, ISO9001, etc etc are the sorts of standardized things that exist (containing things like 'all code must be reviewed'). I think for a browser, if you were Apple and were looking to accept other browser partners, you'd likely do something like this; regular audits of quality, requirements that must be met to maintain access, pentests, basically a continuous process that's to be met by the supplier (similar to how hardware suppliers must meet many requirements).