It's unclear if Bell was more directly copying what he observed in the local schools or if he was merely loosely inspired by them. His own accounts contain only a single, brief observation of local teaching that deals with a non-foundational aspect of his system: "I had, at first sight of a Malabar school, adopted the idea of teaching the letters in sand spread over a board or bench before the scholars, as on the ground in the schools of the natives of this country."[p.24] Despite not giving any credit beyond that, other sources document the existence and prevalence of hierarchical peer drillings setups (the main organizing structure in Bell's system) in various regions of India including the district Bell worked in, so it's almost certain he would have observed this in action.
This footnote is a bit akwardly placed because I'm responding to Gatto's whole claim across these three sections on Indian schooling. His claim is roughly 1) India had advanced social technology for controlling people as part of maintaining the caste system, 2) mass schooling of the lower castes was one such load bearing social technology, and 3) core aspects of this tech were imported to America via England. The first claim is certainly true; claims 2 and 3, however, are pretty tenuous. In regards to claim 2, the distributed network of village schools that other sources describe in the 18th and 19th centuries do seem to have been pretty common and were primarily for the lower castes, the higher castes having their own more expensive schooling network. This mass village school network certainly bolstered the caste system, as the students would only be taught to read and write in the local languages and not Sanskrit (it was still taboo, albeit no longer violently prohibited, to teach Sanskrit to the lower classes, and Sanskrit was the sole language that virtually all of India's accumulated intellectual and cultural heritage was recorded in), and the only things they would read would be devotional literature about doing your caste-based dharma. But ultimately, kids didn't spend much time in this system, and it seems improbable that these schools were pulling much weight in regards to maintaining caste stability. There were endless traditions and customs omni-directionally supporting the caste hierarchy; any child would have been steeped in them for many years before ever setting foot in these schools. So while their schooling was caste friendly, it doesn't feel exemplary of India's advanced social control tech. For claim 3, the only part of what was present in India that clearly transferred to the West was the "hierarchical peer drilling" part, which while somewhat novel and conducive to a strong disciplinary approach, seems much less core to what made the Indian system pro-caste than say the vernacular language restriction, which couldn't have been imported to the West even if desired.