In practice? For me it was the opposite. I worked with a mortgage broker (a professional, not a website) and I got a much better deal.
For startup folks, this is even more common. My current mortgage holder originally denied me credit completely (they were scared of someone working at a startup). My broker knew exactly how to work around this issue, asked me to sign a few forms, made a few calls, and then the same bank came back with the best offer.
Your best bet is to get a few quotes directly, but then to work with a mortgage broker to see if they can beat your best offer -- quite often they can.