Furthermore, I don't recall _ever_ hearing the BBC themselves claim that they were more independant and less biased than other news outlets

No, but they do come close:

All our journalism strives to be impartial, fair and accurate. Our strength is in the depth of knowledge in our journalism, the quality of analysis and range of subjects, original first hand reporting and investigations from around the world...

...BBC News is respected both in the UK and around the world for the strength of its journalism and impartiality. Since the first radio news bulletins almost 80 years ago, BBC News has become the first place people turn to during big news events.


http://news.bbc.co.uk/aboutbbcnews/hi/this_is_bbc_news/newsid_3281000/3281229.stm

I would definitely trust the BBC news output above any other news service I have come into contact with.

They can prise the BBC from my cold dead fingers, or something like that.