In the musical The Sound of Music, these are the pronunciations used. "Doe: a deer, a female deer... Far: a long, long way to run, Sew: a needle pulling thread... Tea: a drink with jam and bread..." etc. I think the song is called Do-Re-Mi and Julie Andrews' accent makes them make sense.
Yeah, I explained it in my other comment, but it's a pronunciation thing. I'm not a native english speaker and I pronounce "saw" differently. I also do not know the lyrics of the song past "re".
I have literally never heard it pronounced saw. Sew is the most common English pronunciation (see the song from Sound of Music), and I've also heard "sol", as in actually pronouncing the L (albeit typically clipped). But "saw" sounds to me like a pronunciation you'd only get with a very particular kind of vowel merger, one which would probably make "so" and "saw" the same anyway, rendering the question pointless.
After saying it aloud to myself several times, I realized it's a language/pronunciation thing. As a non-native english speaker, I pronounce "sew" with a more closed mouth and pursed lips, instead of how native speakers say it with a more open mouth and rounded lips. I also don't know about the song lyrics past "re".