The reason Kirk interfered (apart from the fact that two of his crewmen were incorporated) was that the society was not a living one, protected by the first directive, but a stale, dead one with no change or evolution happening in thousands of years.
One might argue with his logic, but if starfleet has upheld it as valid it makes sense for them to prevent the planet to be taken over by what might as well being alien technology, something so removed by the current societal and technological level of the planet and that has already shown its aim to be freezing the planet in a mid 20th century-like society with no progress, evolution or free will whatsoever.