Not the BBCs Copyright
The thing is the BBC don't own ALL the copyright to (more or less) any of their TV programmes.
The BBC buy the rights to show it on TV a certain number of times and have an agreement that lets them make it available for up to seven days online but their deal doesn't extend beyond that.
Basically for every TV show every piece of music played has several rights holder, the writer retains rights, the actors all retain the right to claim repeat fees - even conductors on musical score retain certain rights.
None of those groups would let the BBC offer any TV show without DRM as offering it without DRM is the same as offering it forever and that would reduce the fees they get for DVD sales.
The IP restriction is there to stop people outside the UK using the iPlayer - in the same way FOX, Disney, NBC, ABC et al stop me using their on demand services over here - it's not directly anything to do with rights.
I agree that the BBC would be better to create their own open source DRM solution that would work cross platform - maybe they could work with ITV and Channel 4 to create one all UK broadcasters can use?