Art,
I think the issue as with all ecological / evolutionary issues is that they take time. If we wait until all the evidence is in, its probably too late. Pollution, melting ice caps, rising sea levels, habitat destruction, are issues that if we take a snapshot are irrelevant but take a time lapse and its a different story.
Similarly here and probably with greater difficulty, as I pointed out, not only because the very practice may make evidence difficult to obtain but also its an area that doesnt readily attract finance for research.
So lets look at it logically. The importance of bird song to reproduction and social interaction is inescapable.
The next question then is, are we interfering with that process when we use recorded song?
We wouldn't use it if it was ineffective! "Bird Song Biological themes and variations" by Catchpole and Slater outlines many areas of research that suggest that we may be interfering with the learning and production of song. You ask if it is populations / individuals etc. Fledglings in learning their song appear to reject similar calls that have no effect - maybe we are influencing the population in an unwanted direction to the point where mating may be interfered with?
My point is the "maybe" . Global warming has its sceptics even with the preponderance of evidence. Do we have to wait for a calamity to unfold before we are convinced, - or should we look at the balance of probability based upon the logic of the situation.
You ask for an example. Thomas & Thomas "Birds of Australia" p73 (Frogmouth Publications 1996, ISBN 0 9528065 0 9) refers to the Rufous Scrub-Bird at a popular rainforest retreat, O'Reilly's in Queensland and notes that thousands of people all over the world try for this bird but it is no longer co-operative.
Anecdotal evidence is likely to be the only evidence for many years.