Positivism assumes that the social world exists objectively and should therefore be measured using objective methods rather than subjective ones such as intuition.
I think that 'objectively' should not be confused with 'independently' here. The original question seems to conflate realism with positivism, in my view. The subjective / objective dualism does not help either. Quantum mechanics indicates that it is impossible to separate the observer from the observed. Critical social research methods takes a similar view. Your notion of 'subjective' equaling mere intuition masks the real problems you want to address.
Positivism was a theoretical trend that arose from the need to place equal value on the social and natural sciences. The weight of scientific rigour and systematicity were soon questioned in sociological and cultural analyses. From there, post-positivism arose and we moved from the "experimental" designs of the Natural Sciences to the "quasi-experiments" where randomness and other elements of culture interfered with the scientific rigour of the social sciences.
It is extremely curious to see how even today the objectivity of the "number" that was invented by the Egyptians continues to play an important role in reducing reality. The data supposes a simplified vision of a complex reality, which is why today positivism (as a science of truth) is used very little in favor of more holistic and comprehensive qualitative practices.
Positivists believe that good, scientific research should reveal objective truths about the causes of social action. Positivists prefer to the limit themselves the study of objective ‘social facts’ and use statistical data and the comparative method to find correlations and multivariate analysis to uncover statistically significant ‘causal’ relationships between variables and thus derive the laws of human behavior.