I have not followed the CBS controversy, however the ill-judged actions of a few individuals at the BBC in a single event hardly cast a huge shadow of doubt across the reliability of a service which has served the public with objective, comprehensive and frank reporting for decades. This is why I call "mired in serious, credibility-challenging controversies" an exaggeration - the BBC controversy did virtually nothing to challenge the credibility of the service whatsoever, in either the domestic or oversea sense.
QED can only apply here if you are using it to highlight that the sources cited have been shown to be non-objective. If you're purporting that their objectivity is a matter of opinion, then ending with QED means nothing and could be misleading.
But of course