This is not necessarily true. It depends entirely on the shape of demand. By way of simplified example, imagine that there are two types of consumers equally distributed: those willing to pay $1000 and those willing to pay $100. Unless you can distinguish at time of payment between these users and charge them different prices (without possibility of resale), you will always be better off forgoing half of the market and charging only the higher price.
It's possible that the business has estimated things incorrectly and is acting suboptimally, but I think it's as least as likely that they are maximizing profits the way we'd expect a rational business operator to do.