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.
This is a tricky issue, because the person asking the question is not you.

You may think some question, as it is stated, is so trivial that it can't possibly be what the person meant. But that judgement is coming from someone with *your* experience and expertise — someone with much less experience and expertise may very well be stumped on this trivial issue!

Sometimes, even a person with experience and expertise just makes a mistake or overlooks the simple thing.

Recall the story about the teacher who declares something trivial, and when questioned in class takes a 30 minute break to work through things, and then comes back and announces "yes, it is trivial" and continues on.

I would estimate that at least 10% of the time I post a "disingenuous" answer, it happens to be exactly the answer the originator was looking for. And there is no harm in posting it even if the question as written is not what the poster intended, because others will still come along and answer alternative guesses as to the intention and engage in comments to try and clarify the question.

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Incidentally, I get far more complaints on the flipside of this issue — when the literal interpretation looks like a 'reasonable' question to ask, but reading between the lines suggests the intended question is something else, I often get a lot of flak for trying to address the something else when everyone else is answering the 'reasonable' question.