Keep in mind that we're talking about prices here. What is a stock price?
If I put in an order to sell one share of GOOG for $1, would you start to believe that the market price of GOOG was $1 per share?
A market price is only as valid as the degree of consensus. Increased liquidity means that there is a high degree of consensus about the current price. This means that one can feel additional confidence that one is getting a fair price.
The main concept to think about here is an order book. Think about the psychology behind orders that are a ways away from the best price (both bid and ask). Those parties are willing to transact, but at a premium. In other words, they prefer to hold unless a sweet enough offer is made.
Thus, for a very large order one has to pay that premium.
