Not true. The broker's job is to hand off your order to Mm's and record the activity that follows. There are dozens of mm's, all with their own spread. When your order drops into the mm pool, those that have a spread that meets your order will automatically begin processing your order. There are no people involved - it is only computers, a fully automated system of trading. Brokers have absolutely nothing to do with how your order is filled, and they can't single out an mm to handle your order.
If your order is a market order, they ALL can be involved in processing it, because, as a market order, ALL of their spreads meet the requirement.
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