**Core Concept**
The hypoglossal nerve (cranial nerve XII) is a motor nerve that supplies the majority of the extrinsic and intrinsic muscles of the tongue, except for one muscle that has a different innervation. This muscle plays a crucial role in swallowing and speech.

**Why the Correct Answer is Right**
The palatoglossus muscle is one of the muscles of the soft palate, but it is unique in that it is innervated by the vagus nerve (cranial nerve X) via the pharyngeal plexus, rather than the hypoglossal nerve. This is because the palatoglossus muscle is primarily involved in elevating the pharynx and larynx during swallowing, a function that is distinct from the other muscles of the tongue.

**Why Each Wrong Option is Incorrect**
**Option B:** Genioglossus is a prominent extrinsic muscle of the tongue that protrudes the tongue and is indeed innervated by the hypoglossal nerve.
**Option C:** Geniohyoid is an intrinsic muscle of the tongue that assists in elevating the larynx and is innervated by the hypoglossal nerve.
**Option D:** This option is incorrect because there is indeed one muscle of the tongue that is not supplied by the hypoglossal nerve.

**Clinical Pearl / High-Yield Fact**
The palatoglossus muscle is an important landmark for the pharyngeal plexus, which is a complex network of nerves that provides motor and sensory innervation to the pharynx. Understanding the innervation of this muscle is crucial for identifying potential sites of nerve damage or compression.

**✓ Correct Answer: A. Palatoglossus**