STiD isn't paid for by the license fee. I'm not particularly fussed about any of the American stuff but it's not as simple as you are trying to make out. We in the UK directly fund the BBC which is why people get protective.
Well, BBC America is not funded by people in the UK, like the Regular BBC is. BBC America is funded through advertising, and Doctor Who revisited is produced and created by Americans working at BBC America. If BBC America was creating special episodes of Doctor Who, that only Americans got to see, then that would be something to be angry over
But Doctor Who Revisited wasn't created by or for Brits, or with UK tax money, so they aren't getting cheated out of anything. They can't be angry at BBC America for taking its own initiative to make this series, and if they want to be angry, then it should be directed at the regular BBC for not doing the same thing.
It is the standard BBC that gets criticised for stuff like this, America isn't getting blamed.