Yes, because people with more money than they need will easily absorb the higher prices even if they have slightly less more money than they need.

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.

Well if people already have enough rice, then presumably they would spend the extra money on other goods that they don't have enough of.

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.