Why did the dinosaurs die out?

The other day (cannot now remember where but I suspect QI), I heard someone ask this question:

Why did the man who invented the weather forecast think that the dinosaurs died out?

My suggested answer was:

Because they did?

In fact, the answer was supposed to be:

Because they were too big to fit on the ark. 

You see the problem here. I have (some might suspect wilfully) misinterpreted the scope of why. I understood it as referring to the verb phrase think that the dinosaurs died out, and so asking why he thought that. It in fact referred to the verb phrase died out, and was asking why they died. The why-question could be asking about either of these things, as in both cases the corresponding because-clause would be at the end of the sentence:

The man who invented the weather forecast thought that the dinosaurs died out because they did (in fact) die out.
The man who invented the weather forecast thought that the dinosaurs died out because they were too big for the ark. 

The difference in meaning comes about because of a difference in the syntactic structure. We can't see or hear this, but it's there. I've colour-coded the clauses here to make it clearer what belongs to what:

[The man who invented the weather forecast thought [that the dinosaurs died out] because they did (in fact) die out]

[The man who invented the weather forecast thought [that the dinosaurs died out because they were too big for the ark]]

In both cases, the man who invented the weather forecast thought something. In the first example, he thought that the dinosaurs died out, and we also get to hear the reason why he thought that. In the second example, he thought that the dinosaurs died out because they were too big for the ark (and all of that is one single thought).

I think that I was led towards the interpretation I chose because of the presence of that, which is optional here. When it's present, because it doesn't have to be there, my little brain wanted to assign it some job, and that job was to kind of turn the clause it introduced into a finished-off unit (that is a declarative clause introducer). So my little brain said 'it is a fact that the dinosaurs died out. Why did this man think that this thing happened?'.