I'm not Frank, but if I had to guess, I would say that it measures the partial frequencies at first just to calculate that particular note's inharmonicity constant. Once you change the fundamental pitch, the actual partial frequencies matter very little because the inharmonicity constant allows you to estimate them easily (and accurately) enough based on what you tune the fundamental pitch to for an excellent overall tuning. From a data efficiency standpoint, it makes more sense to just store the fundamental frequency and inharmonicity constant of each note rather than 12+ partial frequencies.
