What this "person who has made a few interesting claims" appears to be arguing is the Averroist tenet that there is one collective soul for all humans (i.e., that humans do not have individual souls).
According to the OED, an Averroist is
One of a sect of peripatetic philosophers who appeared in Italy some time before the restoration of learning, and adopted the leading tenets of Ibn RoshdRoshd or AverrhoesAverrhoes, an Arabian philosopher born at Cordova, viz. that the soul is mortal, or (as others stated it) that the only immortal soul is a universal one, from which particular souls arise, and into which they return at death.
The Church has vehemently opposed Averroism in part because (1) Catholics must believe that God creates a unique soul for each human (a human is an unique soul + body), and (2) Averroism destroys all moral responsibility for an individual's actions.
For an excellent refutation of Averroism, see St. Thomas Aquinas's short work De unitate intellectus contra Averroistas (On the uniqueness of intellect[ual soul] against the Averroists).