^ But that wears out your already worn, front tires faster if you're not going to eventually rotate them (which in theory also voids the warranty on the new ones), so eventually they'd be on the rear anyway.
I know that many places make this statement to put new tires on the rear but their reasoning is terrible. If the replaced tires had not worn more than the ones staying on the car, you'd have no new tires yet, and have to drive below a certain speed to stay safe, whatever the conditions dictate. Putting new tires on either the front or rear, you stay just as safe staying below that same speed in the same conditions.
If the old tires staying on the vehicle are really that much of a risk, they should be replaced, not gambling on which axle to put them on, not assuming any kind of loss of control is acceptable. It's kind of strange that people don't consider that.