There are some real tight constraints and the Easter Egg in question is a voice over. In fact you could say that this particular treat is yet to be discovered because, well, they 'cheated'.
Former DICE dev Thomas Danke was responsible for the voice-over work in Battlefield 3. He recorded a very special message to play regarding a fellow dev at the time.
Basically you had to be on the US side, be within a certain distance of a spotter who also had to be within a certain distance of a hostile AA vehicle, and even after all that there was a slim chance the VO would fire. The Easter Egg was targeted at fellow former DICE man and now PayDay 2 dev David Goldfarb.
How than did this Easter Egg get uncovered? Someone diligently went through all the extracted game audio files until they found one that suspiciously carried the name 'Dave'. See the YouTube clip below for the investigative work.