Yours is a broad generalisation, and one that has hurt my career in the past because of senior people who inevitably follow this chain of reasoning: "Indians are good at playing the self-promotion game --> shrikant is Indian, and he's not bigging himself up enough --> he must not be good enough --> meh, average rating, let's move on to the next person".
This hasn't happened everywhere, so I suppose it is down to organisational culture as well.
But also I guess my point is: even if broad generalisations hold "true", it's not cool to apply it to an individual.
To me, performing and excelling at your job should be sufficient to make you visible. In a flat structure you're known as the responsibile party for project X, therefore, the self-promotion is happening automatically, as opposed to a deeply nested structure where your department's name is linked to the success of project X, and within the department your team takes the credit, and to be visible you'll have to actively self-promote.