Not sure what you are saying. It is chance how close they are. It works out fairly well in 12 tone scales, worse in most others. Is "coincidence" the wrong word? Maybe. But it didn't have to work out that way, luck or whatever you want to call it was involved.

Just intonation is based on intervals that are ratios of small whole numbers.

The 12-tone equal temperament scale is historically a development of just intonation (a "fork" in software terms).

So it's not a coincidence that 12-tone equal temperament intervals are close to ratios of small whole numbers.