Market-making means providing both a bid and ask for a given asset, so anyone who wants to trade has at least one person who is willing. Lots of different people/institutions make markets, or help to make markets. Some of them employ armies of quants, some do not.
The market price is a bit of a nebulous term. It can refer to the most recent price at which things trade, at the best bid/ask available, the midpoint of these, or something else. Historically, one measure of "the market price" is what the market-maker was offering, though superior prices could be had from other traders in many cases. From the perspective of a market maker, it's not clear what market price they would look to that is better than what they are offering.
Why might market makers seek information quants could provide? Market-makers are in a tough position: They want to offer an ask and bid that enclose the true price so people both buy and sell from them in something like a steady state. When they trade with someone, that person may have superior information about what the stock price is doing, which may mean the bid and ask are no longer appropriate. Suppose you have a bid and an ask and someone buys a bunch from you at the ask. Does this mean the stock price is moving due to a change in the underlying value or was it just noise? This will affect whether you change your bid and ask. If you don't react properly, you stand to lose money. In fact, any time you trade with someone who has superior information, you are on the losing end of that trade. If you are, yourself, informed, you can mitigate these losing situations and try to change your bid/ask before trading with people who are more informed than you are.
Analysis of market-maker behavior is an important topic in microstructure theory. The seminal model by Kyle 1985 ("Continuous Auctions and Insider Trading", Econometrica) is kind of the starting point in this complex literature. The bottom line is that market makers, like everyone else, stand to gain from having knowledge about the "correct" prices beyond just what is observable in trades that have already happened.