Good question. Shows you are doing your research.
Here are some things to consider.
1) Mortgage brokers generally charge less for loans because they don't have the overhead that banks must pay for. Also, they get their rates from several wholesalers, some of whom may be offering better rates than banks.
More than half the home loans in this country are now done by mortgage brokers.
2) However, when you are dealing with someone online, there is a matter of trust. Here's something you might consider, go to mortgage brokers in your town with your request. Mortgage brokers generally have the same wholesalers so your local mortgage brokers should be able to match that rate, if it is legitimate. Try two to three different ones.
3) If you find a few who match that amount, get a Good Faith Estimate. That estimate will show you all the charges and fees. While a mortgage broker might offer you a great rate, you have to check to be sure he is not charging you a "hidden" fee.
4) After you get the estimate, ask the mortgage broker for references. Get names of local real estate agents, not just someone who could be his friends.
5) You can also go back to the bank and see if they will match the rate. Sometimes they will if they want the business. Don't believe the rate is fixed, they have flexibility. Also, if you have a big account with them, let them know. Sometimes that will give you leverage.
6) As for the broker not getting a commission, that is questionable. Most brokers do get commission. Sometimes they get it from the wholesaler. But this sends a red flag up for me. I don't care if they make a commission, I understand why they should. But don't lie to me.
7) Will they bait and switch at closing time? That is a tough question. There is that risk. The more you have in writing, the better. You can also report the broker to the state licensing commission in your state. But if you go with a local broker with good references, you probably have less risk. Although even that person could pull a fast one. If they do, you always have the option of walking away. It would be a pain, but at least you won't have to get stuck.
Good luck and I hope this helps. I think the more questions you ask and the more brokers you talk to, the better you will do. Just settling for the lowest "teaser" rate could be risky without doing any homework and talking to other brokers.