Is this a flaw in JavaScript's prototypical inheritance model?

Is this a flaw in JavaScript's prototypical inheritance model?

I've been learning prototypical inheritance in JavaScript from John
Resig's Secrets of the JavaScript Ninja, and I was wondering what happens
in the following code example (that I just made up).
function Person() {}
Person.prototype.sayHello = function() {
alert("Hello World");
}
function Ninja() {}
Ninja.prototype.swingSword = function() {
alert("I can swing my sword.");
}
Ninja.prototype = new Person();
var ninja1 = new Ninja();
As far as I know, the result of all of these lines of code is that the
variable ninja1 references a Ninja object, that through its prototype, has
the swingSword method, and through prototypical inheritance of Person's
prototype, has the sayHello method.
Where I am confused is in the following: since the property swingSword
(which happens to be a method) was attached to Ninja's prototype before a
person instance was assigned to Ninja's prototype, wouldn't the swingSword
property/method be overwritten by the later assignment of the Person
instance? If not, how can Ninja's prototype property, which references the
prototype object, reference both the Person instance, and have a
swingSword property?