With that being said, it seems appalling that it is possible on Rumblefish side to claim copyright on bird songs, assuming that they have vetted the audio personally.

Then again, should we not say that the algorithm that processes for copyrighted audio is imperfect and therefore could be improved further to not have false positive such as this?

I would bet that someone would have copyrighted sounds such as cash register's ka-ching!. Although use of such sounds from a specific recording should be copyrighted, I should be able to record a video of a real world cash register without anybody in the world claiming my work to be theirs.