This has happened before in my prototype, but I chalked it off to my inferior post production skills when doing the first sound clips. The new sound clips, however, were pristine, I was sure of it.
So the problem had to be somewhere else. Changing a suspect in my trigger script did not change a thing.
Yet turning off 3D Sound in the Audio Importer Inspector did the trick: no more weird squeaks.1
Of course, there are situations where you would need the 3D Sound property set. I have yet to test this out. Maybe the squeak only occurred because my Audio Listener was so close to the Audio Source.
Of course that meant turning it off for almost 60 clips by hand, since there is no such thing as bulk change in Unity … *grml* ↩