Question: Is it in the spirit of Stack Exchange to always make a sincere attempt to interpret the OP's intentions? I believe it is.

Precision is important in maths, and where questions are imprecise it will often be helpful to address that imprecision. However I frequently see answers or comments which pick some logical fallacy or inaccuracy within a question, then to declare the question answered on the basis of it, while making apparently minimal attempt to interpret what the OP intended.

I think it's important to interpret the OP's intentions and to address the question they *intend* to ask, rather than some technicality. We will all have seen perhaps the stupidest example of this, in which the next number in some sequence is proposed by some method which can generate infinitely many candidates all having equal claim.

I am in favour of such stupidity attracting a waterfall of downvotes from the community.

Answer: 
I think it can be helpful, **in a comment**, to point out that the question, as read literally, has a trivial answer. This may help the asker to understand what assumptions or requirements may be missing. 

For instance, given the question:

> 
> Does there exist a topological space $X$ such that every continuous $f : X \to \mathbb{R}$ is constant?
> 
> 
> 

I might comment:

> 
> Yes, you could take $X$ to be a single point, or equip $X$ with the indiscrete topology. Perhaps you meant to require that $X$ should contain at least two points and be Hausdorff?
> 
> 
> 

But I would not post it as an answer; I would not claim that it answers the question; and I would not upvote such answers.
Although I agree with the premise that we need to interpret in the best interest of the OP, your point with downvoting is debatable due to a couple of reasons:

1. Interpreting (or, sometimes, guessing) intent takes time and should have been the OP's role.
2. If you ask answerers to interpret, there is bound to be misinterpretation, even in good faith.

On the other hand, the benefit of interpreting is largely for:

1. pedagogical reasons, which will likely...
2. guide the user to clarify or provide additional context and maintain a satisfactory post.

That said,

* It's the [ultimate responsibility of the OP to clarify their *exact* intent](https://math.stackexchange.com/help/how-to-ask).  

Appropriate flagging and review actions should be done just like on any other post.
* The OP needs to engage with the commenters and work towards the OP's intended goal.  

In such cases, commenters should put forward constructive criticism instead of tongue-in-cheek responses.
* When illustrating a point, balance and don't extend too far.  

Interpretation may not be agreed by all (including the OP) and might even be annoying if not properly presented. Think twice before offering interpretations. When not sure, engage with the OP!

These are my thoughts and opinions after engaging in one such recent post. I tend to enforce these three bullet points whenever I comment, ask, answer and vote.