This answer, as @AdamWood comments, is entirely accurate and correct, but doesn't answer the question asked. But the reason it doesn't answer the question asked is because (according to the text of the answer) the question is based on a false assumption, and thus cannot be answered as asked.
Is the answer still an answer? Should the question be revised in light of the answer (which however does need citation support)?
In trying to find a balance between the current "Answer the exact question asked" and attempting to provide helpful answers, my thought would be that it's OK if handled correctly.
Example question:
Since Christians believe that the earth is only 6000 years old, how do they think all the different species evolved in such a short time?
The question starts with a false assumption: that all Christians agree on the age of the earth.
In my opinion, it would be fair to answer this as follows:
Your question assumes that the earth is 6000 years old. There are various views including {blah blah}. However, there are groups that believe and teach that the earth is 6000 years old, including {list of groups}. According to {one of those groups}, {rest of answer with citations and quotes here}
In other words, it's fair to address the false assumption, but if the question is answerable from an accepted perspective, and you can provide a good answer, then provide that answer after clearing up the assumptions.
It takes skill to give a good on-topic answer to an off-topic or poor answer. Take it as a challenge and e sure that no matter how Truthy or off-topic the question is, if you choose to answer it, do so in a way that your answer is in line with the site's guidelines.
If the assumptions are bad, or it's impossible to answer the actual question, don't answer it! Vote to close it.
If the answer doesn't attempt to answer the actual question at all, but only addresses the false assumption, then goes off on another tangent, then no, it's not OK. It's not an answer.
If the answer addresses the false assumption and also answers the actual question, then it's just fine.
Often pointing out a false premise is entirely the proper thing to do in answering a question. The question, "Can God make a rock so large he can't move it?" can only be answered this way, for instance.
However, in the example you pointed out, the answer is really just an extended comment about the question. It appears to me that the answer is saying "you used the wrong term!" which is really a comment. In this particular case, I think it would be appropriate to delete the question as 'not an answer'--or perhaps convert it to a comment after editing for brevity.
It would also probably be okay to leave the answer as it, and let the downvotes speak for themselves.
It's also worth noting that whether Catholics have altars (or shrines or anything else) is also immaterial to this question. The question is about other denominations, and that question is still completely valid, and can be answered (and asked) even if the assumption about Catholics is wrong.
TLDR; In general, answers ought to be permitted to challenge a question's premise, but in this case, it's NAN, and should be a comment.
One of my most well received answers to a question was this:
https://christianity.stackexchange.com/a/11366/1039
The answer I gave highlighted 3 "faulty" premises. At the time, I also said this:
Despite my answer in which I pick out three "faulty premises," I still +1d this as a good question. Theology often involves uncovering hidden premises and exposing them. Please don't be offended. Welcome to C.SE!
As long as the faulty premise being corrected really is in the question, then yes, the answer is totally on target.
Update: Another very well received answer here
Isn't reincarnation affirmed by the Bible?
Did the exact same thing.
I think this depends on how flawed the premise are.
Suppose, for example -- and I'm going to use deliberately silly examples because I don't want to get sidetracked in serious debates -- suppose someone asked, "How many animals did Abraham bring on to the Ark?" Well of course it was Noah and not Abraham, and any answer that accepted the false premise and went on to talk about Abraham loading animals on the ark would be wrong. But it would be easy to fix the problem with a sentence, like "I presume you mean how many animals Noah brought on the Ark, in which case ..." and then go on to answer the real question.
But it's easy to imagine questions where the premise is so flawed that the question cannot be answered as stated. Like if someone asked, "How could Jesus have been executed by the Romans when he lived hundreds of years before the Roman Empire existed?", it is difficult to see how one could give a direct answer to the question. The only possible reply is to say that Jesus did NOT live hundreds of years before the Roman Empire existed.
Then there's a middle ground where I think the question becomes tougher. What if someone asks a question based on a premise that is debatable or controversial? Like suppose someone asked, "Given that science has proven that evolution is a fact, there was death and suffering before humans evolved, and therefore before Adam sinned. So how can Adam's sin be the cause of death and suffering?" It seems to me that there are two quite different ways one could answer the question. One way would be to try to reconcile the Christian doctrine of Original Sin with evolution. The other would be to challenge the idea that evolution is true, i.e. to challenge the premise.
To an extent I think this depends on the wording of the question. Suppose the OP acknowledges that a premise is debatable, and then phrases the question as, "For those who are convinced that X is true, how do they reconcile that with Y?" In that case I think challenging the premise would be irrelevant and non-responsive.
But what's the difference? I think a key point is that if they question implies that the premise is universally-accepted fact, the OP may not realize that it is, in fact, debatable. Other users who read the question and see answers that all talk as if the premise was accepted fact may also leave with a wrong impression. But if a question acknowledges that he is starting from a debatable premise, this issue goes away.
