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: 
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.
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.