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 that sincere attempt is part of what a good answer requires.

I frequently think I know what the OP intended even though it's not what the question says. If the question is otherwise reasonable (shows effort, ...) I may answer (or comment), beginning

> 
> I think you mean ... if so
> 
> 
> 

sometimes, with just a hint when I think I can help the OP solve the problem her/himself.

When this strategy succeeds it helps everyone: the OP learns and the moderators have less work managing the close queue.

I (too) dislike (snarky) answers that are correct because they rely on the literal but clearly unintended meaning of the question.
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.