It helps to split rancidity into its two stages and test the reason against each stage separately.
Stage 1 is enzymatic, lipase in the bran hydrolyses the rice oil (triglycerides) into free fatty acids (FFA). Stage 2 is oxidative, those free fatty acids react with oxygen to form aldehydes and ketones, the compounds that actually smell and taste rancid.
Parboiling's steaming step (around 100 degrees Celsius) denatures the lipase enzyme, so Stage 1 barely proceeds during later storage. With little FFA being produced, Stage 2 has little substrate to work on. That is why parboiled rice stays fresher for longer, confirming Assertion (A).
Now test Reason (R) against this picture. Antioxidants such as tocopherols and oryzanol act by slowing Stage 2, they mop up the reactive species that cause oxidation. Studies on parboiled rice actually show these compounds surviving, and even migrating into the endosperm, rather than being destroyed. So the mechanism named in (R) is not what is really happening, and it is not the reason rancidity is lower.
Assertion true, reason false describes the situation exactly.
\[\boxed{\text{(A) is true but (R) is false}}\]