Ever try that at a Chevy dealership? I did recently. Looked at a Transverse ($41,000) and was told they don't haggle. The price is what the sticker says. Drove the Transverse and it is woefully underpowered. Was told by the salesman that I was the first person to say that. Great big SUV with a 6 in it. GMC's Acadia is the same. The GMC dealer seemed more willing to haggle, tho. Can't imagine why they put sixes in them.
It's kinda funny how the business changes. You see more and more automotive dealers saying they don't haggle then other companies who have set prices who are willing to haggle. You can even haggle at places like Home Depot even though they have fixed prices. The haggling takes more effort in that case, but you can do it.