Right. The Church recognizes the principle of subsidiarity which is not coincidentally part of its social teaching.

Modern media has allowed the pope to receive unceasing attention that the papacy never possessed historically, but what is important to emphasize is that this is not a reflection of how the Church is administered or how authority is distributed. The idea that the pope is "running the Church" or "watching every member of the one and a half billion member flock like a busybody hawk" is a fiction drawn from jejune ignorance. Rome is notoriously slow to act, which should in general not be seen as a sign of incompetence, but as an expression of subsidiarity. It is much better to view the pope as the ultimate referee rather than some oppressive overlord. The moral ball is in your court, as it were.

W.r.t. absorbing what's around it, the Church has always recognized logos spermatikos or seminal reason, meaning, it recognizes reality as an intelligible creation of God, it recognizes the inherent rational nature of every human being, and thus it recognizes that every human being has an in principle capacity to recognize and know reality, to one degree or another. So, it sees no reason to suppose that there is nothing good or true or beautiful outside the Church and plenty of reason to recognize it and embrace it. What is good is good, what is true is true, what is beautiful is beautiful. When the Church encounters a culture, it seeks what is good within it and seeks to transfigure it in order to rescue its goodness and perfect it. Gratia non tollit naturam, sed perficit.