this is correct, and the reason we are tolerant is because of dispersion: even though the different harmonics are present on the same string of the same length, the resonant frequencies don't need to be integer multiples of the fundamantal since waves of different frequency have different propagation speeds on the string.

in the case of bowed strings mode-locking ensures the phases of all the harmmonics are reset each cycle (the bow sticks and slips), so that bowed instruments can be played harmonically to parts per billion.

since a lot of sounds are plucking we must be tolerant for frequency dependent propagations speeds in regular strings / media