**Core Concept**
The intrinsic muscles of the hand are a group of small muscles primarily responsible for finger movement. The median nerve is a major nerve that innervates many of these muscles, playing a crucial role in hand function. The question requires knowledge of the specific intrinsic muscles and their nerve supply.

**Why the Correct Answer is Right**
The median nerve supplies most of the intrinsic muscles of the hand, including the thenar muscles (abductor pollicis brevis, flexor pollicis brevis, and opponens pollicis), the lateral two lumbricals, and the first and second dorsal interossei. However, the intrinsic muscle not supplied by the median nerve is the adductor pollicis, which is supplied by the ulnar nerve. This is because the adductor pollicis is involved in thumb adduction, a function primarily controlled by the ulnar nerve.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is not provided, but typically, common intrinsic muscles supplied by the median nerve would be incorrect.
**Option B:** This option is not provided, but typically, common intrinsic muscles supplied by the median nerve would be incorrect.
**Option C:** This option is not provided, but typically, common intrinsic muscles supplied by the median nerve would be incorrect.
**Option D:** This option is not provided, but typically, common intrinsic muscles supplied by the median nerve would be incorrect.

**Clinical Pearl / High-Yield Fact**
Remember that the median nerve supplies most intrinsic hand muscles except for the adductor pollicis, which is supplied by the ulnar nerve. This knowledge is crucial for diagnosing nerve injuries and understanding hand function.

**Correct Answer: D. The adductor pollicis is not supplied by the median nerve, but rather by the ulnar nerve.**