Be more assertive when unit testing (and not when challenging me)

I tweeted this today.

A test without an assert is not a test. It leaves the intended behaviour as completely ambiguous.

Apparently I'm wrong. Some people disagreed. They were mistaken.
Let's examine their arguments.

Argument #1: Name the test method clearly enough and you don't need an assert?

public void Should_not_throw_when_doing_that_thing()
{
        var obj = new MyObj();
        var result= obj.doThatThing();       
}

To me this this has a huge gap missing in it. I'm a fan of the AAA pattern when constructing tests. Above we are only doing the Arrange and Act part.  This is why I'm not a fan of the [ExpectedException] attribute. There is no assert within the body of the message. It just doesn't read as I expect to be.

Argument #2: A test can contain no assertions, if you are mocking interactions.


[Test]
public void WhenDoingSomeThingWithAnotherThingThatWillOccur()
{
    var someThing = MockRepository.GenerateStub();
    var anotherThing = MockRepository.GenerateStub();

    someThing.Stub(x => x.Do(1)).Return(2);

    new myObj(someThing, anotherThing).Do(1);

    notificationSender.AssertWasCalled(//blah);
}

Ok this is a good point but when you are interaction testing you are still asserting that a behaviour is true. Its even there in the code.

As you can tell I'm not convinced. Can anyone provide a compelling reason to leave asserts out of tests?