Actually I think it is more case for the opposite. As a market-maker I regularly priced and executed trades for large hedge funds: Brevan-Howard, Pimco, Bluecrest etc. Being in a position to see their executed flow allows you to take a view on whether you think they are correct or not, either in establishing new positions or taking-profit or stopping out of existing positions. Large hedge funds have dedicated research and resources to analyse markets so the outcome of that analysis can be quite valuable, particularly if the fund is consistently profitable.
Of course, you have to prioritise the execution of the customers order, but after that there are no restrictions on how to position your own book in anticipation of new orders or potentially new market movements within the scope of your risk limit.
Of course the other answers relating to pure market-maker activity nicely document the difference between market-making and proprietary trading