Of course one can accept the claim, the article is explaining the misunderstanding people seem to have surrounding rejecting claims, i.e. if there are two possible outcomes and one rejects A then they must accept B. That is simply incorrect. Let me explain using a different example, the judicial system. I am going to use Scottish verdicts as they make it easier to understand and the verdict of “not proven”…
"Not proven is a verdict available to a court in Scotland. As with other judicial systems, the burden to prove guilt rests with the prosecution.
Under Scots law, a criminal trial may end in one of three verdicts: one of conviction (“guilty”) and two of acquittal (“not proven” and “not guilty”).[1][2]
Historically, the two verdicts available to Scots juries were that the case had been “proven” or “not proven”. However in a dramatic case in 1728 the jury asserted “its ancient right” to bring in a “not guilty” verdict even when the facts of the case were proven (see jury nullification). As the “not guilty” verdict gained wide acceptance amongst Scots juries, Scots began to use “not guilty” in cases where the jury felt the “not proven” verdict did not adequately express the innocence of the person on trial. Shrewd defence then further encouraged this interpretation in order to persuade juries unwilling to bring in a “not guilty” verdict that the “not proven” could be brought in as a lesser or “third verdict”.
The result is the modern perception that the “not proven” verdict is an acquittal used when the judge or jury does not have enough evidence to convict but is not sufficiently convinced of the accused person’s innocence to bring in a “not guilty” verdict. Essentially, the judge or jury is unconvinced that the suspect is innocent, but has insufficient evidence to the contrary."
So in court there are two possible circumstances…
The defendant is guilty
The defendant is not guilty
The claim is the defendant is guilty, if there is not sufficient evidence for one to accept that claim then they can reject it without accepting the defendant is innocent (which is the opposite of the claim). Just like if someone is throws a coin of a cliff then claims it must be showing tails, given I do not have sufficient evidence to evaluate the claim I can reject it without believing the coin is showing a heads.
It really is important that people understand this concept as it is a basic principle, yet critical component, of rational thinking.
Do the thought experiment yourself. I have just thrown a coin out my window I have no idea what side is landed on but I am going to assert based on nothing but a guess that it is showing heads. Do you accept my claim that it is 100% definitely showing heads? (Clearly the answer has to be no), does that mean you are claiming it is 100% definitely showing tails?