My example shows that precedence has no effect on the operator evaluation order.

Not quite true. * is evaluated before +. (Which makes a difference for overloaded operators)

And since associativity breaks ties in precedence, how could it possibly have any effect on the operator evaluation order if precedence doesn't.

You're right here. After reading betterworld's comment I thought that the right associativity of the = operator was the key, but it isn't. It seems to be just a special case for =.