No you don't need a licence. If you only use the iPlayer it doesn't count unless they start streaming live broadcasts of the BBC networks. You can write and tell them that you don't have any television receiving equipment and they will send someone round to check it out.
"Therefore, if you are using your PC or laptop solely to watch TV programmes from the BBC iPlayer service in its current form, you do not need to be covered by a TV Licence."
They stream some programmes live - Match of the Day for definite as you can only watch this on iPlayer whilst it is being shown live on TV.
I never understand why people have a problem with paying the license fee. Go to another country, the US being a good example, watch their TV networks and then you'll never complain again.
One point with the TV license is that it doesn't give you the right to own and watch BBC programmes in perpetuity - just to watch them when they are broadcast (keeping a recording for a long time isn't technically legit). This is why there is the 7 day limit on watching programmes through iPlayer and why you have to pay normal prices for DVDs.
I reckon Apple and the BBC will be able to work out some kind of deal. Apple providing BBC content through iTunes to UK residents for free and selling it in other countries (at least the programming the BBC can sell).
Apple would be stupid not to work something out as it will sell Apple TV's and iPod's by the case. Though no doubt the other UK networks will complain.