The classical music companies crying "unfair" to the BBC aren't questioning the copyright of the BBC's Beethoven performances. They're complaining about something far sillier that is only possible because they deal in public domain product.
The BBC is providing product for free that other companies charge for. The companies that charge for their product say that is unfair.
Much like people complain that Microsoft is unfair because they provide most of their software for free. The complaint only comes up at all because the BBC is a large respected media company that are direct competition. If they suddenly provide excellent classical music content for free, other classical music companies could be out of work.
I still say stiff shit.
To explain the stupidity of such companies, let me point you to an article I discovered today (via various places, but I'll reference acb):
a group of French cleaning ladies who organised a car-sharing scheme to get to work are being taken to court by a coach company which accuses them of "an act of unfair and parasitical competition".The women, who live in Moselle and work five days a week at EU offices in Luxembourg, are being taken to court by Transports Schiocchet Excursions, which runs a service along the route. It wants the women to be fined and their cars confiscated.
Is there a single person in the world who doesn't think this is inhuman?