...should I trust my initial reaction, which says that the sax player is just not very good?
Yes! It's played by someone who by their own admission can't play the sax - producer and engineer Graham Massey:
"At that point, I was still recording with Biting Tongues, which had
turned from a normal band into a sort of electronic duo with a
jazz‑influenced saxophone front line. Howard Walmsley, who played the
sax in Biting Tongues, had left his soprano from a session the night
before, and so I picked it up and just had a go. I'd played the
clarinet and was a bit of a have‑a‑go saxophone player, but I was not
a real saxophone player. Still, I could crank out a melody, and I
think my limited ability made it what it was."
(From Sound on Sound magazine).
In accordance with that 'experimental' attitude, I would imagine that it was simply played until the result was pleasing to Massey's ear, with only secondary consideration for whether or not it was in tune by some standard. Personally I rather like the intonation - I think it contributes to the somewhat melancholy, otherworldly feel of the track - but with this, as with everything else in music, de gustibus non est disputandum!
As a more general point, being (arguably) "out of tune" is something that is done deliberately in modern music in all sorts of contexts, for all sorts of reasons - whether it's simply the use of equal temperament, or blue notes being bent through a whole semitone, or the honky-tonk piano (and other chorus effects!), or rappers singing deliberately off key because being too in tune wouldn't sound 'street' - it's all out there.