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No need to speculate, they explain how this works right on the main page of http://pizzaforcoins.com :

"We set our exchange rate APPROXIMATELY $0.50 Cents less then the current Mt.Gox Rate. The reason for this is that with rapid fluctuation of rates and occasional drops, we do not want to be left holding a worthless bag if the rate drops for some reason. We update prices on a daily basis to reflect this 50Cent rule."

I imagine stores counter that by setting the price in USD on the server side, and then using an API to convert it into bitcoin on each page view. Problem solved.

So they constantly change the price then, albeit automatically.

Wouldn't this be an issue any business that offers prices in more than one currency experience?

Bitcoin is unusually volatile. The exchange rate of eg. USD to EUR is much more stable.

Much more stable, yes. But it still fluctuates as much as 4% on a daily basis.

Wouldn't they just charge a flat price in BTC and then only sell it on the market for USD when the exchange is high?

Good luck timing the market...