Surely that's only true in the short term while supply of the good stays constant. Long term you'd expect supply of the now in-demand good to increase, bringing prices back down.
In the context of rice...We already produce more rice than people can eat, so there's no driving force for supply to increase. Increasing supply would only make more rice go unsold. It's not like just because you have more money now you biologically need to eat more volume too.
Unless the price of rice goes up. If they're buying rice now instead of something else with limited funds, that suggests that they need the rice more. Goods aren't all perfectly exchangeable. If you need shoes, a shirt won't protect your feet.
