**Core Concept**
The patient's inability to extend the fingers and thumb of the right hand after radial head excision is due to disruption of the extensor mechanism at the wrist, leading to a lack of extension of the metacarpophalangeal (MCP) and interphalangeal (IP) joints. This is a classic example of an extensor tendon injury or rupture.

**Why the Correct Answer is Right**
The extensor pollicis longus (EPL), extensor digitorum communis (EDC), and extensor indicis (EI) tendons are responsible for finger and thumb extension. These tendons are innervated by the posterior interosseous nerve (PIN), a branch of the radial nerve. The radial nerve's motor branches supply the muscles responsible for finger and thumb extension. After radial head excision, the patient's wrist is left in a flexed position, putting tension on the extensor tendons, leading to a possible injury or rupture. The lack of sensory deficit indicates that the radial nerve's sensory branches, which supply the back of the hand, are intact.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect as it does not relate to the patient's inability to extend the fingers and thumb. Median nerve injuries typically result in thumb opposition and flexion deficits and are associated with sensory deficits in the lateral three and a half fingers.

**Option B:** This option is incorrect as it does not address the mechanism of injury. The patient's symptoms are due to a direct injury to the extensor tendons, not a nerve injury. The radial nerve's motor branches are responsible for finger and thumb extension.

**Option C:** This option is incorrect as it is not directly related to the patient's symptoms. The brachioradialis muscle is involved in forearm flexion and is innervated by the musculocutaneous nerve (C5-C6), not the radial nerve.

**Clinical Pearl / High-Yield Fact**
The posterior interosseous nerve (PIN) syndrome is a common complication of radial head excision, leading to extensor tendon dysfunction. This condition is often due to nerve compression or injury during the surgical procedure.

**Correct Answer: C. Brachioradialis muscle injury is not the cause of the patient's inability to extend the fingers and thumb.**