Wouldn't that mean that both have the exact same responsibility? A bug in the FE, would essentially render the BE unusable, and therefore would cost a lot of money and time as well.

For example; if Amazon's checkout button somehow broke, and prevent users from checking out, it would also cost a lot of money.

EDIT: to give a more visual example, if Amazon changed their checkout button to a different color and style. It could potentially cost them millions, because it might not entice users to click it.