It's not only that. When adjusted to population size, India does very poorly, worse than China, Korea & Co. but also much worse that Russia and Romania.
As a former participant (from a small country, so it was easier to get in), I should note that IMO problems are not a good representation of general education in a country. They are very specific, wildly different from both high school and university mathematics. So success on the IMO is much more dependent on the individual's and the country's level of preparation for the specific event. IPhO, for example, is much more similar to the physics we learn at school, except the problems are more difficult.