**Core Concept**
The mandibular nerve, a branch of the trigeminal nerve (cranial nerve V), provides sensory and motor innervation to various structures in the lower face and jaw. It is crucial to understand the precise distribution of its branches to accurately identify the nerves supplying specific muscles and structures.

**Why the Correct Answer is Right**
The buccinator muscle is primarily innervated by the buccal branch of the facial nerve (cranial nerve VII), rather than the mandibular nerve. This is because the facial nerve is responsible for the motor supply to the muscles of facial expression, including the buccinator, which aids in the formation of the cheek and assists in mastication. In contrast, the mandibular nerve supplies the muscles of mastication, including the masseter, tensor tympani, and temporalis muscles. The buccinator's innervation by the facial nerve is a key distinction in the anatomy of the facial and trigeminal nerves.

**Why Each Wrong Option is Incorrect**
**Option B:** The masseter muscle is indeed supplied by the masseteric branch of the mandibular nerve, making this option incorrect.
**Option C:** The tensor tympani muscle is also innervated by the mandibular nerve, specifically through its tensor tympani branch, making this option incorrect as well.
**Option D:** The temporalis muscle is supplied by the deep temporal nerves, which are branches of the mandibular nerve, making this option incorrect as well.

**Clinical Pearl / High-Yield Fact**
In evaluating the innervation of facial and jaw muscles, it is essential to distinguish between the motor supply of the facial nerve and the sensory and motor supply of the trigeminal nerve, particularly the mandibular nerve. This distinction can be crucial in diagnosing and managing conditions affecting the muscles of facial expression and mastication.

**✓ Correct Answer: A. Buccinator**