It's not completely upto the BCCI though. The Australian and England boards also have a lot of power over the ICC since they are part of the Big-3.
Although Australia and England are in the Big 3, ICC earns the most from the Indian market. As a result, ICC flexibility towards India is more than others. Yes, they also have value as Big 3 countries but comparatively India dominates the most in world cricket and also in ICC.
We can't term it to be flexibility, because these three countries always make a combined decision. Because, moving ahead with a self plans could countries togo against the board and unite the rest of the cricketing boards that are just with ICC for name sake. The small boards need to unite to make some changes.