**Core Concept**
The posterior column of the spinal cord is responsible for transmitting sensory information, including proprioception, vibration, and fine touch, through the medial lemniscus pathway. This pathway involves the dorsal columns of the spinal cord, which are crucial for transmitting these specific types of sensory information.

**Why the Correct Answer is Right**
The correct answer is not affected because the posterior column primarily transmits information related to proprioception, vibration, and fine touch through the medial lemniscus pathway. This pathway bypasses the posterior column and involves the dorsal columns of the spinal cord. As a result, lesions of the posterior column do not directly affect the transmission of these specific sensory modalities.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because lesions of the posterior column can affect the transmission of proprioception, vibration, and fine touch. These modalities are transmitted through the dorsal columns, but the posterior column plays a crucial role in the medial lemniscus pathway, which is responsible for transmitting these sensory modalities.
* **Option B:** This option is incorrect because lesions of the posterior column can affect the transmission of pain and temperature. While the spinothalamic tract is primarily responsible for transmitting pain and temperature, the posterior column also plays a role in the transmission of these modalities through the anterior spinothalamic tract.
* **Option C:** This option is incorrect because lesions of the posterior column can affect the transmission of crude touch. While the posterior column is primarily responsible for transmitting fine touch, it also plays a role in the transmission of crude touch through the dorsal columns.

**Clinical Pearl / High-Yield Fact**
The posterior column of the spinal cord is responsible for transmitting sensory information related to proprioception, vibration, and fine touch through the medial lemniscus pathway. This pathway bypasses the posterior column and involves the dorsal columns of the spinal cord.

**Correct Answer:** D.