I think it is the pronoun that is in a possessive case which is used to show ownership of something.
The type of evidence that Schlosser uses in this excerpt is anecdotal. By definition, anecdotal evidence is based on stories that may or may not be true but due to lack of hard facts. They are usually based on personal stories. In this case, there is no proof that things mentioned in the excerpt happened the way that they were described.
