You're not specific on why, so it's hard to address this point. The case study clearly stated that the sax was warmed up then tuned to middle C on a standard tuner. Why middle C and not concert A or some other note? Because it's roughly in the middle of the instrument and we don't know it's intonation yet. We find out later whether middle C was a good note on which to tune that sax/mouthpiece combination, once we've completed the study (spoiler: it wasn't).
I try to put it short:
Considering that a saxophone is necessarily a compromise, when it comes to tuning
Also assuming that someone can play with a really "neutral embouchure",
There are two separate aspects to tune:
- the instrument's lower register
- the octaves
Generally speaking, the mouthpiece volume affects the lower register, the length affects the higher register (the theory of the missing cone is more of a theory for making mouthpieces than a direction for tuning)
Length: since it affects short notes (C2) more than long notes (C1), a "short" instrument will have a sharper C2 than C1
Let's say that we found a position
Narrow octaves will want a longer tube. (keeping in mind that some notes are wrong anyway) But this will affect the previous ste, so it is necessary a compromise.
Talking about octaves, D1D2 is a troubled octave, as is A1A2, so I wouldn't rely on them to tune my octaves.
F1 F2 is ideal: its octave pip is in the correct position, as is the one on B2B3, but the shorter pipe of B is more prone to embouchure variations.
In practice:
- I play the lower register, making sure that I don't lip up or lip down excessively a register (I do anyway)
- I check the octaves, expecting F1F2 to be nicely in tune
- I check with the tuner
If most of the notes are flat or sharp, it may be the wrong mouthpiece for the horn, so there is no point in continuing
If most of the notes are about in tune, I can start checking tuning tendencies (as in your study)
In your case F1 F2 were out of tune and most noted were sharp
There is one more issue on low instruments (I had some enlightening conversations about contrabass saxophones and clarinets):
We often hear harmonics rather than fundamentals, as does the microphone of the device (300-3400 Hz).
An F#1 on a bari is 110Hz, the tiny mic is probably unable to understand it. I noticed most tuners going really funny on bass clarinet.