Most of the websites make it very clear in their sales process that placing the order is not a sale, and that the sale isn't legally completed until they verify the order. If a website doesn't do that, then yes, they should be required to honour the price they charged your credit card or bank account.
Being sloppy with your website is bad enough; being sloppy with your legalese is unforgiveable. If you don't have the good sense to have your terms and conditions vetted by a lawyer, you should pay for your stupidity, not the customer.
I'm not at all surprised The Brick refuses to honour the prices they post. Every single time I've thought about purchasing something from them, they started tacking on extra fees and charges during the process, and I ended up telling them to go fuck themselves and walked out the door. They are beyond doubt the greediest scam and con artists in the furniture industry I've ever had the fortune of not dealing with to completion of a deal.
The worst is a scam they were charged with and spanked for by the courts in Canada -- the "no money down" deals where you were expected to pay service and financing fees up front. To their twisted minds, because those weren't the actual charges for the furniture itself, they were free and clear to screw you over before you even took shipment. Thank God the courts stopped that nonsense -- you notice they haven't run a "0 money down" "sale" in Canada for a couple of years now that they've been spanked.