When you apply for a mortgage, you don't get your mortgage directly from Fannie and Freddie, you go through a Broker or Bank, who charges a fee for qualifying you and obtaining financing for you from Fannie and Freddie. Although we all get the same rate and credit from Fannie and Freddie, the pricing is up to the lender and or broker. How much credit am I or the "Lender" keeping and how much are we sharing with you if any? That is what impacts the rate and closing cost tied to that rate. So yes, shop until you drop and let me know how you did.
For example, So Lame Bank offers 4.375% rate with 0 credits to you and $900 in closing cost. So Cool Mortgage offers you the same rate with a 1% credit to you more than covering all closing cost making it a no cost loan other than the rate being charged.
How can Michael provide better pricing than the big banks? Efficiency, the more efficient your lender is, the less they need to charge. Even if they charge $0 on the front, they are charging something on the back end. The less they charge on the back end, the lower your rate and the more credit you get if any. The most efficient lenders don't need to buy leads, they get referrals. ;)