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.
Is a point of this site to help to socialize mathematics? How great is our obligation to help those learning to express themselves with mathematical precision? There is a broad spectrum of compassion within the user community. Some obvious homework questions are answered immediately. Some closed immediately. Do we want to have a site that welcomes mathematical explorers, or do we want to enforce discipline and rigor?

Most of the responders have mathematical skills, and they are stripped of social tools when a question is stripped of tone and context when encoded to a string of letters. We are reduced to inference, to guessing. Some users think poorly formed questions should be rebuffed. They may argue that condoning such behavior enforces bad habits. Some users try to add value and provide help not just for the OP, but anyone who looks at the question later.

Do we want the site diluted - or polluted - with extraneous questions? Or do we want to embrace the community at large, and accept a need for maturation? The site rewards users for removing poorly received questions. Should the reward be increased? Should the trustees of the site be entrusted to cull low value material?

The countervailing currents swirl.