The article cited by the questioner incorrectly represents the limited amount of historical evidence that we have about the incident described. When the article is compared with the evidence, it can be seen that its account has been extensively fictionalized. Thus, it is an unsuitable basis on which to question anyone's truthfulness -- except perhaps that of the author of the fiction, whoever that was.
Quoting from the article cited by the questioner, "Newton ... claimed he had been unaware of the challenge until he first saw it at 4 pm on 29 January, some 5 weeks after its publication." "He further claims that he solved it by 4 am the following morning..."
Most of that is fictional embellishment. Thus, there are two different historical sources about the incident, but they tell us much less about the incident. Both are reported in the notes given in D T Whiteside's edition of Newton's 'Mathematical Papers', vol.8, pp.72-3.
All that Newton is known to have said or written about the background was (original in Latin): "I received yesterday ... two copies (published at Groningen) of problems ...". (Nothing more than that about the background, he then went on to quote the problems, and to give his solutions.) The document is a letter from Newton dated 30 January 1696|97 (also given in full in the 'Correspondence of Isaac Newton', vol.4 from p.220) in which he sent the solution to his friend Montague, who was then President of the Royal Society.
There is a source for the 'late-night' aspect of the story, but the source was not Newton. It makes a big difference to put a reminiscence from years after an event fictitiously into the mouth of a person other than its source. The source here was Newton's niece, Catherine Barton, who lived with Newton after he moved to London to be Warden of the Mint. Newton's niece seems to have organised his domestic and social life until she married. Her recollection was recorded years later by her husband, Newton's friend John Conduitt, who noted that his source for the reminiscence was his wife. She also told her husband about Newton's characteristic behaviour (quoted too in Mathematical Papers vol.8 p.73): "when [he was] come from the Tower" [i.e. where the Mint was located, he] "would stand still a great while if any book or paper [had been] sent him[,] before he would eat". (This kind of intense focus on Newton's part was also separately reported by his amanuensis of the 1680s, Humphrey Newton, whose reminiscences of Newton's forgetfulness to eat or sleep while concentrating on a problem has often been quoted, e.g. by R S Westfall in 'Never at rest', p.406.) There doesn't seem to be anything implausible or out of Newton's character about the reminiscence given by Newton's niece to her husband.
What has happened with the story quoted by the questioner, as shown by its comparison with the sources, is that an incident that we can barely glimpse from proper historical sources has been given fictional embellishments (here by some person unknown), and then the fiction itself has been used to draw conclusions about the incident. This has nothing to do with history or historical investigation: it more closely resembles the peddling of false gossip or juicy scandal. (It is to be hoped that the source from which the questioner cited the embellished story will be properly amended before too long.)
