I agree. However, instead of bluffing, just walk and don't go back.
Totally agreed. The problem with price matching is that the broker/lender that's putting it all on the line to cut a great deal get's nothing but shopped, so over time they disappear.
Also, important to note NAB will do better deals direct if your relationship and negotiation is good enough than if going through a broker who has no influence/skill.
However if your broker has clout (this is an individual mortgage broker thing rather than a particular brand of broker, so more likely amongst smaller players), then you'll probably do better there.