Yes or no what?

I was sort of half-heartedly watching ITV's 'This Morning' programme while I was working yesterday (honest) and they were talking about vigilantes. They had one of those viewer polls, where viewers have to text or tweet their opinion about an issue and either the result is an equal split or it confirms what we already knew. 

This was the question put to viewers about this 'issue': 

Perfectly reasonable question. Two opposing points of view to choose between: either vigilantes have a valid role (in the process of catching criminals) or the job of catching criminals is one that should be left to the police alone. Choose the position you agree with and tell ITV. 

But here's how the results were presented: 

Well, yes or no what? Yes, either vigilantes have a valid role or catching criminals should be left to the police? And no, neither of the above apply? 

Clearly not. Obviously, what they meant was yes or no to the first part of the question (do vigilantes have a valid role), as this clearer presentation shows:

Probably no one except me was confused by the wording. I've spent more time than most people thinking about questions over the last few years, though, so I noticed this strange construction. 

The question was presented as if it was an 'alternative question': one where the answer is one of the alternatives that are mentioned in the question. More everyday examples tend to have smaller parts of the sentence given as alternatives, as in Are you coming for lunch or tea? The answer is either 'lunch' or 'tea'. The question from ITV had two whole questions as the options: Do vigilantes have a valid role? and should catching criminals be left to the police?. 

This kind of alternative question, as far as I can tell, is hardly ever used as a real alternative question (as the lunch or tea example is). More often, the second part isn't a real alternative, and you aren't meant to pick one of them as the answer. Instead, the question is really a 'yes/no' question, or one where the answer is either yes or no. You can't answer yes or no to a real alternative question (where # means that the utterance is strange in some way): 

Did you buy that suit or hire it? #Yes.

But in the poll above, and in most cases of apparently alternative questions with two entire questions as the 'alternatives', the answer can be yes or no, showing that they must really be yes/no questions. But! You can also answer by providing one of the alternatives. This is sort of the case for yes/no questions as well, in a trivial sense which I won't go into here, but it's different with these strange halfway things.

This was actually pointed out to me pretty early on in my PhD (by Sten Vikner), who gave an example like Have you done the washing up or have you just been sitting in front of the TV all day?. The question provides two alternatives, and you can answer it by providing one of them as the answer, but it's really just asking Have you done the washing up? and it's more natural to answer with yes or no. I didn't really address this problem then, but perhaps I ought to now.