> This is bound to rile up natives rather soon as oppression and loot are the only objectives.

it was a lot more complex than "natives" vs the East India Company. In many places they replaced Mughal rulers who were not natives either. Some groups of natives supported them in order to get rid of rulers or existing oppressive systems (or they did not care because it made little difference to them).

> Norman invasion of England or Mongol invasion of China where the invaders fused with the local culture.

The Normans fused gradually, over time. Longer than British rule in India lasted. There were many cultural influences both ways, as can be seen in language, cuisine, political and legal institutions. British people who remained in India became Anglo-Indians, and much the same happened elsewhere in the Empire.

Local rulers who descended from Mughals were largely considered natives. Taking Siraj-ud-Daulah as example, it's true that the Local population was happy to see him go(at least the non Muslims were) but he was definitely considered a native, especially when compared to Europeans.

The key difference I was trying to highlight with my comment was assimilation vs extraction. By early 19th century, it was pretty clear among British polity that India is to be treated as a colony for resource extraction and nothing more.