A claim of possibility or impossibility are both claims about the nature of the universe and both require evidence.
If you have no evidence for a claim, then any statement made regarding that claim, either in support of or opposed to, is arbitrary and lacks any intellectual value.
For example, any claim about the (non)existence of god is arbitrary and not worth even a moment of consideration, because there is no evidence whatever in support of the claim either way.
I suppose there are two different claims of possibility that are getting confused.
There is a hard claim of possibility, that is a claim of the state of nature (e.g. it is possible for a photon to travel at 0.5c). This hard claim is one where we definitively say that it is _certain_ that it's a physical possibility.
Then there is a soft claim of possibility, that is a claim of our state of knowledge. (e.g. It's possible that Rob went to the store, but I'm not sure).
These are two different claims. One is a hard claim that should only be made with evidence. The other is a statement of our uncertainty and an open mind; that doesn't need any evidence to make.
It's a shame that these two different meanings of these words exist, but such is the English language. They are saying that their research does not close the door on that eventuality, and that their state of knowledge on that topic is uncertain.
If I ask you, "Where did Rob go?" and you, having never even heard of Rob, respond "he might be out cheating on his wife," it would be an arbitrary statement bordering on malice. Qualifying the statement with "but I'm not sure," doesn't help you, because even the suggestion of the initial possibility needs to be based on evidence.
If, instead, you know Rob well and you happen to have a general understanding of his schedule and needs, you might respond with "It's possible he went to the store; last night he mentioned he ran out of toilet paper." This is an evidence-backed claim.
A claim about the state of nature is the same. Your knowledge leads you toward certain avenues of research, so you might think, "photons have properties x, y, z, so maybe they can travel at .5c, let me look into it." However, it would be improper to base your research on whim, like "I think photons are little gremlins and they run really fast, but can they run slow too?" Such a claim is not a claim about reality, it is arbitrary.
Claims about the world must be grounded in knowledge, and knowledge must be based on evidence.
> photons have properties x, y, z, so maybe they can travel at .5c, let me look into it.
No, the claim about what is possible for a photon was much stronger. I am asserting now that photons can travel at .5c, full stop. I will not look into it, as I have already determined it is possible. I am not making a hypothesis about the universe, I am making a claim about how I believe it to actually work. Anyway, that is an aside.
I still think this just comes down to semantics about what is a claim about the world and what is a statement about uncertainty.
I interpret them saying something is possible as them making a statement about their own partial knowledge. I specifically do not interpret it as a claim about the world. I do interpret it as a claim about their own research and their own partial knowledge.
Their research does not demonstrate an impossibility. That is the claim they present. I still believe you are making a semantic interpretation of the word "possibility" that is different from the intent of the researchers. I think you are interpreting a stronger claim than the researchers are making.
Here is, for example, the same qualification as reported in a different article:
> Although, in this study, the researchers found that commercial cognitive training alone would not have an influence on one's decision-making process or cognitive abilities, they believe that it was still an avenue worthy of rigorous investigation.
If you have no evidence for a claim, then any statement made regarding that claim, either in support of or opposed to, is arbitrary and lacks any intellectual value.
For example, any claim about the (non)existence of god is arbitrary and not worth even a moment of consideration, because there is no evidence whatever in support of the claim either way.