To say the BBC is without a capitalist agenda is not a lie, it is a debatable point. I think what the OP meant to point out was that the BBC is not a commercial operation (it has a commerical arm - BBC Worldwide - but this has no bearin on its main operations). It does however operate within a capitalist society and is subject to capitalist pressures, even if less so than, say, ITV or Sky. It also has a public charter, which is subject to review and renewal by the governemnt every ten years. It is a public service broadcaster, meaning a broadcaster intended for public benefit rather than to serve purely commercial interests.
(It's worth noting, btw, in all the fuss over GBBO going 'commerical' on Channel 4 that although C4 is a commerical channel, it ALSO a public service broadcaster. Their remit is similar to the BBC's, though narrower. Channel 4 has traditionally been required to cater for 'minority audiences' which they have traditionally loopholde by providing programming for the minority of 'youth'. Hollyoaks counts as 'minority interest'. Seriously.).
The BBC is undoudtedly without problems and even guilty of real wrongdoing, but to me it's ridicuous to list their fuck-ups and imply this list makes the BBC not worth funding to continue.
The BBC is not a Perfect Cinnamon Roll. That doesn't make it Evil Mega Corp. Whether you fall on the side of thinking the BBC is largely a force for good or bad (if it even makes sense to think of such a vast and varied coorporation being able to be one or the other) listing a load of things the BBC has done wrong does not amount to take-down of them as a coorporation. Of course the BBC has commited wrongdoing and made mistakes. That is not an argument for why the whole thing isn't worth preserving. There are surely valid arguments to that end but a list of instances of bad behaviour isn't that argument.
Furthermore many of these points are pretty subjective; the BBC has been accused of both a pro-Israeli and a pro-Palestine bias on many occassions, usually in equal number over the same reportage.
Am I saying any such complaints are unfounded? Of course not; I don't believe the BBC is politically unbiased or has never commited any wrongdoing as a coorporation. But I believe these are the mistakes and weaknesses of an institution that is imperfect but on the whole honestly striving for Reithian values, and achieving the greater spread of information, entertainment and education through its actions. I think the world is better rather than the worse for the BBC existing.
More to the point, paying your licence fee is a LEGAL REQUIREMENT if you watch BBC programming (that includes via iplayer since September) and don't pay you can be take to court and given heavy fines. Not paying it is like not paying a tax; I might not agree that my taxes are going towards funding wars as well as hospitals, but I don't get to opt in and out of it according to personal ethics. You either watch pay it and watch, or don't pay it and don't watch. Watching while witholding the fee is not a political statement.
Or you can see it as not paying for a service or product you use. I don't support Nestle as a company. That doesn't mean I steal Milky Bars from the shop while decrying the company, it means I don't buy OR consume any Nestle product.
(And actually there really is a debate to be had around the handling of the licence fee; I believe there should be more compassionate exemption for poor, elderly and housebound people and think its pretty appalling that those who honestly can't afford face court action.)