What? The UK charges a license fee on television and radio receivers in order to fund the BBC, but that fact has nothing to do with whether or not BBC broadcasts can be received in North America.
No it does. British law specifically states that the license fee that UK customers pay for the BBC cannot be used to fund transmission/receipt beyond the borders of the UK. In other words, the money that has been received from UK citizens, can't be used to pay for feeds to other countries who don't pay this fee.
BBC 1, 2, 3, 4, Prime, and other BBC channels can be received over the European continent on the Astra satellites, but there is nothing set up (nor will there be) to transmit the BBC feeds to North America. If you are a commercial company and you fall within the satellite reception area of the Astra satellites, you can get BBC channels for local re-distribution, but that is only possible because the satellite already covers most of Europe, no extra money needs to be spent there.
There are commercial channels through which feeds can be purchased (think sporting events, news events, etc), but there is currently no provision to receive the actual BBC channels anywhere in North America.
BBC America is really an American commercial venture that buys, among others, British TV programming from the BBC, ITV, Channel4, and other UK TV stations.
It will also directly go against the commercial interests of BBC America, and BBC Canada (as well as American TV producers who have sold shows to the BBC for viewing in the UK) if the BBC itself would be able to broadcast to the North American continent.
As a resident of both Europe and the U.S., I also know that the reverse is also not possible: One cannot receive anything from Dish, DirecTV, or other American satellite providers, even if you lug all your 110v equipment over there, and use a satellite dish that is 30 feet wide.