Usually ほど is used to refer to some degree/extend that is in some way high, or even approaching/reaching some upper limit.
Given how precise(※) and reserved Japanese usually is, I find it surprising how「なるほど」 is used as a casual(＊) interjection meaning "I see.". I would rather have expected it be sound overly confident, in the sense of "I see/understand/... it now crystal clearly".
Looking at the etymology from gogon-allguide (and other sites):
unfortunately doesn't really answer my question.
Am I fundamentally misunderstanding the meaning of ほど here, or is なるほど simply an overstatement? How come that this is used so casually(＊), where Japanese is usually so precise in it's statements(※)?
(※): Since this seems to be misunderstood, here's an elaboration:
I mean precise in the sense of accurate, not in the sense of definite. So for example when one does not necessarily know something exactly, or does not want to express too much confidence, it is common in Japanese to in some way express that (等・くらい・みたい・よう・そう・…), instead of making a definite statement that might not be correct.
While this at times is purely used for politeness, the sentiments of statements never overstepping what one actually knows seems to be common throughout the language.
And in that vein, my wondering about はるほど originates.
(＊): I do not mean casual in the sense of casual Japanese (in opposition to polite, or literal Japanese), but rather casually, in the sense of using it without much thought or meaning behind it, as an interjection in a conversation to respond to the other's statements without really saying much (besides "I follow/understand/... what you are saying" or "This information is new/interesting/...").