Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
What you have concluded following your research in Islamic resources, that this matter is a lie, is correct. This matter is purely a lie. Claiming to know the sins of a particular person in the manner you described is claiming the knowledge of the Unseen. Nobody knows the Unseen but Allah, the Most-High. This is something absolute in the religion of Islam. Allah Says (interpretation of meaning): {Say: "None in the heavens and the earth knows the Ghaib (unseen) except Allâh,…}[27:65]. Allah, who has no partners or associates is the Only One who knows the Unseen.
Allah also Says (interpretation of meaning): {And with Him are the keys of the Ghaib (all that is hidden), none knows them but He……}[6:59].
The people of knowledge authoritatively assert that if a person is asked whether he knows the unseen and he says 'yes,' he is a Kafir. Because what he says denies what the texts have determined. When Allah negates a quality from His creation and confirms it only to Himself, then it is not possible that He have a partner in that quality.
Nothing is reported from the Prophet (Sallallahu Alaihi wa Sallam), or his companions, or the pious predecessors about what your friend is claiming. Far be it from them to claim the knowledge of the unseen. This is just a product of Satan to astray those who lack knowledge and are weak in religion.
As regards logic, it is "A mechanism that protects the mind from error in thinking".
Al-Akhdari said in his book Al-Sulam Al-Murawnaq: 'Logic for the soul is like the grammar for the language, it protects ideas from error, and takes the veil off for a clear understanding.'
The study of logic became demanded by some modern authors for the study of some sciences like the principles of Fiqh jurisprudence, because a lot of its publications are published in a logical form. It is impossible to grasp their meaning except with the study of logic. Some people of knowledge came to the above conclusion, and amongst them Al-Ghazali in his book Al-Mustaspha, as he said: 'There is no confidence in the knowledge of a person if he does not know logic.'
Ibn Sahlan said in his book Al-Bassair Fi Ilm Al-Mantiq: 'The need for the (science of) logic is compulsory.' Al-Damnahuri and Abdel Raheem al-Jundi in their interpretation of the 'Al-Sulam' concluded the same thing.
Muhammad Al-Amin Al-Shanqitti also came to the same conclusion in his book 'Adab Al-Bahth wal-Munadhara'. Abdurraheem Al-Jundi, who explained the book Al-Sulam said: 'The difference (of opinion) is in the logic which is mixed with the sayings of philosophers, as with regard to the pure logic, then there is no one who prohibited to study or teach it.'
Among the books of logic which are free from philosophy is 'Al-Sulam al-Murawnaq, and its interpretation by al-Damnahouri and Al-Jundi, and the text of Issaghougi, etc.
Allah knows best.