Nuts though it sounds, the possibility of fitting tiny spy cameras to migratory birds cannot be ruled out. The use of animals in warfare has a long history. As recently as WWII, the Russians used dogs to destroy tanks by using Pavlovian techniques to train them to carry explosives underneath the German tanks.
However, pigeon racers band their birds and often stamp phone numbers on the birds' wing feathers, and I can well imagine them leaving some fishing line tied to the birds' legs to make them easier to catch if they stray. This was done in falconry.
Occam's Razor, hmmmmm.....
Politically motivated xenophobic paranoia propaganda? They wouldn't, surely.