Take the common attitude to somewhat more contemporary conspiracy theories... They seem far more believable than a scheme like this. Yet the government appears to ratify this story.
Might it not just be a more sophisticated layer of misinformation?
- now your enemy is complacent, secure in the knowledge that you are super super dumb
- now your enemy is on the lookout for dog and cat listening devices rather than the 5th generation bird listening devices
- now your enemy is indeed paranoid about any stupid animal roaming about and has to meet in enclosed spaces
- you, knowing that experimenting on cute cats is unethical, seek to terminate the practice by devising an experiment that fails so embarrassingly as to never be tried again
etc