Absolutely, but more than likely, I think Oversteer's story fits. The installers don't do PR, but they do know that if they have to put on four Brand X tires and can't find them (or they're too lazy to look), and know that Brand Y = Brand X, guess which brand you'll get?
That leaves the front desk to explain why Brand Y were substituted. The labour to replace the tires would be an extra cost to them, so they attempt to rationalize it with the customer. Not the best PR you can do, but we're not talking about large profit margins on these small, non-brand-name tires, either.