**Core Concept**
The question is testing the understanding of the rectoanal inhibitory reflex (RAIR), a reflex that inhibits peristalsis in the rectum in response to rectal distension. This reflex is mediated by the enteric nervous system and involves the release of inhibitory neurotransmitters such as nitric oxide.

**Why the Correct Answer is Right**
When the rectum is inflated with gas during sigmoidoscopy, the RAIR is activated, resulting in the inhibition of peristalsis. This is because the distension of the rectum stimulates the release of inhibitory neurotransmitters that act on the smooth muscle cells of the rectum to relax and decrease peristalsis. The RAIR is an important reflex that helps to prevent the premature defecation of stool from the rectum.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the RAIR is not directly related to the increase in peristalsis. Instead, the RAIR inhibits peristalsis in response to rectal distension.
**Option B:** This option is incorrect because the RAIR is not dependent on the presence of gas in the rectum. The RAIR can be activated by any form of rectal distension, not just gas.
**Option C:** This option is incorrect because the RAIR is not related to the presence of stool in the rectum. The RAIR can be activated by any form of rectal distension, regardless of the presence of stool.

**Clinical Pearl / High-Yield Fact**
The RAIR is an important reflex that helps to prevent the premature defecation of stool from the rectum. It is often used as a diagnostic test for Hirschsprung's disease, a condition characterized by the absence of the RAIR.

**Correct Answer:** C.