We've had both Dish and DirecTV and their satellites are in two different places. The DirecTV satellite had to be installed in our back yard and the Dish in our front, so unless you are completely surrounded by trees everywhere, you may be able to get DirecTV to work.
Also the first time the DirecTV installer came out he said he couldn't get a signal and I was so distraught (long story - something about being poor and deprived of cable tv for years and years) that Mary walked all around the house and figured out on her own a totally different place where it would work. So don't give up hope :)
For what it's worth, we switched to Dish from DirecTV because they offered us a DVR in two rooms which was comparable to what we were paying for DirecTV in one room. However, we've found that the signal isn't as good with Dish and the DVR works terribly on live sports events, so we are planning to switch back to DirecTV when our contract is over. I'm 99% sure DirecTV also has BBC America.
Lis