Maybe the pigeons are refugees? Politically that would make removal difficult! Maybe we should rehabilitate the pigeon so they alter there behavior?
As for the moon, I put cant instead of can sorry. Personally I think if it didnt happen then Russia would have gone all out to prove it didnt happen, I think considering the technology around at the time it was a huge achievement to get off the ground let alone land.
On balance it's probably harder to fake than actually do it, then there would be the issues with keeping all the people involved quiet. So while I would love it to be a conspiracy, I think it did happen and was an incredible achievement. I also think a huge amount of luck was involved, its a shame the space program has been cut back.