It doesn't hold water. It's just a typical form of lenition. plenty of languages exhibit the same phenomenon. The example I'm most familiar with is Irish, where /f/ under certain phonological and grammatical conditions softens to almost nothing (written "fh" to maintain the underlying sound). The interesting thing is that the exact same set of circumstances causes /p/ to soften to /f/ (written "ph" to maintain the underlying sound). The sound didn't go away, but its partial disappearance became grammaticalised into what's called "séimhiú", which is incidentally appropriate as it contains an example of the phenomenon.

So yeah, the hypothesis is most likely bunk.