TL;DR: We should only demand evidence of notability in one direction, and accept genuine disbelief of the claim by the OP as being sufficiently notable in the other.
Underlying your question is an issue about notability which I think has been brewing slowly for a few months, and I welcome the opportunity to thrash it out.
I am going to start off badly - by digressing to a completely different topic.
Are Skeptics On The Side Of Scientific Consensus?
We've had a few people who have been unimpressed when they have found the Skeptics.SE community is not full of people who, like them, think that the scientific establishment trying to maintain its hegemony by suppressing the true facts of whatever conspiracy theory they follow. They complain that we are just blind follower of scientific orthodoxy.
Yes, we tend to accept much of the scientific consensus, because practising scientists generally take very similar skeptical approaches to evidence and theory.
However, science doesn't know everything. (As one wit put it, if it did, it could stop.) There are wrong scientific theories. There are even wrong scientific consensuses. It is perfectly in line with skepticism and science to challenge the theories, and demand evidence for them. (It isn't, however, acceptable to deny, ignore or cherry-pick the facts when they are presented.)
Often, there are lone voices, declaring that the "Emperor is wearing no clothes". Very occasionally, they are right. An important (albeit challenging) part of science and skepticism is acknowledging when the evidence shows your theories are wrong.
Now, let me get back to notability...
Why Demand Notability?
I see at least four reasons for demanding evidence of notability.
1) If we are going to ask people to volunteer their time doing the research and writing up the result, we want them to be doing something that will be useful for many people. So, we don't want them to be chasing up some whimsical idea that someone had in the pub.
2) Providing references to the actual claim helps protect us against fighting strawmen - where we rebutt a misunderstood claim that was never actually made.
3) If we allow random ideas to be proposed for us to research, we are actually encouraging people to spout more speculative nonsense on the Internet, rather than reducing it, which is probably not what many of us would like.
4) Asking the question-writer to spend just another couple of minutes researching the question before they post, we probably help a lot of people to answer their own questions without us.
Direction of Notability?
Now, typically, we have only demanded notability to apply in one direction.
If someone asks a question that goes:
A TV celebrity says "Celery juice can cure cancer". I don't believe it. Is is true?
it is sufficient for someone to post evidence that the celebrity said it, but that the OP is doubtful. We don't ask the OP to post evidence that anyone is claiming the opposite.
If someone asks a question that goes:
A TV celebrity says "Celery juice is mildly dangerous. It can cause chemical burns if it contacts the skin." I don't know whether to believe it. Is it true?
we have accepted this, too. Not taking a position until the evidence is in, is a creditable response from a skeptic.
However, when someone asks a question that goes:
My science teacher says every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Is it true?
we have seen a different reaction from some people.
This question is directly challenging a well-established part of scientific consensus. The response has been to reject the question's notability, until some evidence is shown that anyone disbelieves this claim (i.e. that the counter-claim is notable.)
This meta-question is basically asking the community if that is the right response.
If we go back to our reasoning for notability, it makes sense to demand evidence that the counter-claim is notable. If challenging well-understood science is just a whimsical idea from the pub - a random notion only held by one person - it is justifiable to not bother with answering it until the OP can show that it is notable to disbelieve the claims.
This is particularly true if the OPs themselves do not express a position - if even the OP agrees with the consensus view, scrabbling around to defend it is wasting everyone's time.
One problem with demanding this notability of the counter-claim is the subjectiveness of the demand: Who decides whether the scientific consensus around gravity, or homeopathy, or acupuncture, or about diet, is well-enough established that challenging it is considered a perverse point-of-view?
Another problem is that it dismisses the role of the maverick, who can see the consensus view is wrong, and has evidence to support it. I think the concept that the maverick with the right evidence could overturn the orthodoxy is an important one to skeptics, and we mustn't write-off the claims of mavericks without considering the evidence.
But finally, I see that the burden-of-proof is on the scientists here. I acknowledge that Skeptics.SE often plays loose with the burden-of-proof, frequently putting it upon the answerer rather than the claimant. However, this is a case where the burden is in the right place, for once. If scientists want to make a positive claim that gravity follows Newton's Laws, they should be able to show evidence to support that.
So far, I have been assuming that the question is asked in good faith.
It doesn't happen often, but there are also recalcitrants who don't want to acknowledge the evidence that supports the science. It's reasonable to not bother to arguing forever with such a person.
On a related note: Normally, we can answer questions by pointing to high-quality articles as evidence. Sometimes, we get people who include a reference to a high-quality article (that follows the scientific consensus) in the question, and claim they are skeptical of it. In such cases, it is reasonable to ask what part they are unhappy with, putting the burden back on them.
Finally, in the cases where it is isn't sufficient to cite one or two papers, but instead the onus is to explain an entire discipline of science in an answer to a question, then it is reasonable to redirect them to do some reading or attend a course.
I think that our notability rules should be clarified slightly.
We should continue to demand that evidence of notability should be provided for a claim that the OP is skeptical about.
If the OP, in good faith, claims that they do not believe a claim, we shouldn't demand that evidence that their view-point is notable, even if it flies in the face of scientific consensus. It is reasonable to (politely) question the reasons for their maverick point-of-view, to establish that good-faith.
As before, if the OP believes in the original claim, then the whole question doesn't belong on Skeptics.SE.