Ten days on, and the 18 October edition of Russell Brand's BBC radio show has gained an after-life all its own. The outline by now is well known. Mr Brand, along with his fellow entertainer Jonathan Ross, left a series of crude messages on the answering machine of the 78-year-old actor Andrew Sachs, which were played in their entirety on the programme. Complaints from Mr Sachs's agent produced only a jocular and ambivalent apology from Mr Brand.

Then the story hit newspapers and all hell broke loose. Two complaints to the BBC swelled to 10,000; the BBC apologised and announced an inquiry; Ofcom said it was launching an investigation; the BBC Trust requested a report. The Prime Minister condemned the duo's behaviour as "inappropriate and unacceptable". Who next? The secretary general of the UN? Yet what actually happened? A couple of weak jokes, undreamt-of publicity for Mr Sachs's granddaughter, and an apology that could have laid the whole farrago to rest.

Now there can be little doubt that the routine was coarse, juvenile and vindictive, and the language used in respect of the grand-daughter was obscene. But it is precisely this edginess, this pushing of boundaries, that draws listeners to Russell Brand's shows. This broadcast might have pushed the boundaries somewhat further than others. But of those who tuned in – an estimated two million – only two apparently felt strongly enough to complain. There is an unfortunate element of "Disgusted of Tunbridge Wells" in the subsequent flood of apoplexy. The truth is that regular listeners seemed to take the offensiveness in their stride.

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This raises two questions. The first is whether the licence-funded BBC should be hiring the likes of Russell Brand and Jonathan Ross, at vast expense, to broadcast the sort of material so many people – we would venture to say most – find offensive. The fact that a self-selected late-evening audience finds the programme entertaining, and the BBC arguably attracts a wider audience to BBC Radio 2 as a result, does not invalidate the question. Is this the sort of thing a public service broadcaster should be doing?

The bigger question concerns the BBC's accountability. Its apology on Monday seemed to reflect more a fear of sections of the press than a proper sense of moral obligation. From day one, the corporation has behaved with that confused combination of formality and buck-passing we know so well from the saga of Andrew Gilligan and the Today programme and the distorted editing of the documentary The Queen. Something that should have a simple answer – what was the chain of editorial responsibility and who signed off on the pre-recorded show? – requires a full-blown inquiry. No BBC executive spoke out either in defence or condemnation of the programme. So far, the only name in the frame is that of a very junior editor.

The BBC has enormous departments, long chains of editorial authority and large numbers of highly paid executives who routinely receive "performance" bonuses. Yet when something goes wrong and legitimate questions are raised, every which one of them vanishes into the ether, with the occasional honourable exception, such as Gavyn Davies or Peter Fincham. This reluctance by the publicly funded broadcaster to take responsibility is, ultimately, more distasteful than what went out on its airwaves. If a leaner BBC is too much to ask in the short term, a more responsible Corporation should be imperative.