I agree with Mort, part of the problem with the middle east is they are fed on a diet of anti-western propaganda and conspiracy theory and if we can unpick that by beaming BBC into their homes, then that can only be good. It has often been suggested that Ronald Reagan's hawkish defence policy led to the collapse of the eastern bloc, but for my money it was more a case of rock music and Levi jeans.
Besides, from what I read of that article, none of this money is being supplied by the licence fee payer per se, thus rendering your Grump invalid:
"This comes partly from a UK government grant, and partly from BBC World Service funds freed up by the closure of radio services, mainly to Eastern Europe." (the World Service is funded by gran in aid from the F&CO).