Yes, you're wrong. We don't get a subsidy or any other special treatment from Broadcom; they are helping us in allowing us to purchase chips in much smaller numbers than they'd usually consider, though. They're also very happy for their engineers to volunteer on the project (we have four or five who chip in) - outside work hours.
That's one way to think about it. Here's another: if you were actually able to get this chip from Broadcom (you're not), and asked for a 10K lot (you can't), do you think the price would let you achieve a $25 BOM?