Apart from the absurd overuse of quotation marks that you linked, "remaining scrupulously neutral" is indeed a general editorial policy of the BBC. They tend to "report the controversy" - i.e. report that "some people think A, while others think B" rather than weighing the factual support or veracity of either position.
However everyone still has their own personal biases, and from time to time the hosts do inject their personal positions on the less scripted programs (eg the BBC World Service radio program). I actually dislike this as well, because it's not factually-based or institutionally overseen. It's just a host deciding to mock a position or slam a guest on his own. There is a difference between journalism and editorializing, and I have a particular problem when an institution that has a policy of being scrupulously neutral will refuse to touch factual bias but allows their hosts to go off and editorialize. It's not all that frequent, but it really bugs me when I hear it happen.
Another problem is that there's always bias just from what stories get selected as newsworthy and what positions are represented within them. There's an Overton Window inherently represented by that. Overall I do think the BBC does a pretty good job on that one at least.
As an aside - try watching CSPAN after a big state event or something when they do the call-ins. They have the most hilariously stone-faced hosts I've ever seen. To avoid the appearance of bias they will take literally anyone, and they get the full range of people, both in political opinions and sanity. "I THINK THAT OBAMA IS A SECRET CHRONONAUT FROM MARS! HE..." "Thank you caller. Now to Susan from Rhode Island,...". They must have their emotions surgically removed or something.