Granted that people will assimilate what they hear to the phonemic
distinctions which they are prepared to recognize and their orthographic
system permits them to represent, this calls for skepticism respecting
only the phonetic precision of the transcription, not the distinction
itself. Canadian and Tidewater dialects do not say u: for au in house,
the Welsh name Llewellyn does not start with an "f" phoneme - but
transcriptions like "aboot the hoose" or "Fluellen" do represent real
phonetic differences from "standard" English pronunciations.
As I understand it, historical linguistics systematically relates the
sin/shin opposition (which you concede the Masoretes actually heard) to
phonemic distinctions evident in cognate languages which could not be
realized in the Phoenician alphabet. Whence do you derive the
opposition?