Prices are not handed down; they are the output of many participants acting on private information and constraints. Lit venues contribute most of it because their quotes are public and executable, while dark-pool and internalisation flow largely references prices discovered elsewhere.
This is the central policy argument about off-exchange-trading: if too much volume prints away from displayed quotes, the quotes that everyone else references become thinner and less informative.
Example: a stock's day includes 42 million shares, of which 18 million print off-exchange at prices derived from the nbbo. The midpoint those crossers used was set by roughly 24 million shares of lit competition. Remove the lit side and there is no midpoint to cross at.
Related: lit-market, off-exchange-trading, nbbo, indicative-price