The story they have cleverly created about Hinduism goes something like this: Hindus were too occupied with earthy pleasures and pursuits to develop an authentic spiritual and philosophical tradition of their own; therefore, whatever Hindus find valuable in modern day Hinduism has either been imported from elsewhere or conceals something pathological that can only be exposed through Freudian psychoanalysis.
Since it is brought up in the essay, I want to just mention something about the idea that the Bhagavad Gita is a Buddhist work.
The Gita is embedded in the Mahabharata, which today is a stupendous epic of over 100,000 verses - we are told seven times as long as the Bible, ten times as long as the Illiad and Odyssey combined. Its original core was probably of the order of 8000 verses, so you can understand the accretion over the ages.
So it is entirely possible that the Gita is a later interpolation. I think in the opinion of most philologists it is indeed an interpolation.
To this I want to add that it is an interpolation of an extremely interesting kind. One of the themes in the Mahabharata that we have today is the evenhanded treatment Krishna gives his warring cousins, Arjuna and Duryodhana. In the Mahabharata minus the Gita, however, I think only Duryodhana is vouchsafed a Vishvarupa darshan (vision of the cosmic form) of Krishna, this when Krishna is trying to dissuade him from war. Arjuna has his darshan only later, during the exposition of the Gita, when the first battle is about to fought. So the interpolation of the Gita had to be accompanied by a reaching back into the story and making an interpolation there as well - it is inconceivable that in the story before the Gita, only Duryodhana had this privilege and not Arjuna.
So this was not some random appropriation of some work, it was sewn into the story in a seamless way.
Even if it is some later expansion of an earlier tradition that simply said, Krishna had to inspire a dejected Arjuna to fight, i.e., there was a placeholder in the original story, the coordinated addition of vishvarupa darshan had to have taken place to the epic.
A remark about the quest of philologists for the "original" work and what it meant - in my opinion, this is based on a mental model of the Bible as the original word of God. Firstly, Indian traditions are much more malleable/much less canonical, and second, the reason for preservation of the tradition, handing down from one generation to the next is more likely because of the meaning of the text in the living tradition, and not some "original" meaning that is anyway obscured, and that the traditionalists were blissfully unaware of.
What I'm asserting is that to understand the Indic traditions, one has to take seriously the tradition itself; its (long-forgotten) origins have very little to say.
The philologists want to understand your grandfather purely from his first year of life, but what your grandfather has of interest to tell you comes from his accumulated life experience.