When examining, do not forget that the price of the option is also function if the IV of the option (the two are not really separable). There is NO magic.
IMHO: It was helpful to me to consider BSM as a good way to express a single point, with zero unknows. If you provide the correct inputs, it can provide valid output. (Garbage in Garbage out) Most common mistake is failure to provide the correct quantity for the volatility input! The proper volatility input is the input that results in the proper price (with all other inputs being also precise). The error then becomes related to the difference in the "price" you assume, to what the real price should be (which may not have the precision desired for illiquid strikes), but is close enough for very liquid products/strikes.