Step 1: Understand the task. We must find the FALSE statement about opioid antagonists.
Step 2: Check option A. Naloxone, especially in poorly absorbed oral or peripherally restricted forms, blocks gut opioid receptors and relieves opioid induced constipation without reversing central analgesia. This statement is TRUE.
Step 3: Check option B. Naltrexone reduces craving and is an approved treatment for alcohol dependence. This statement is TRUE.
Step 4: Check option C. Nalmefene is long acting with a half life of around 8 to 11 hours, much longer than naloxone, whose half life is only about 1 to 2 hours. This statement is TRUE.
Step 5: Check option D. On a milligram basis naltrexone is actually more potent and longer acting than naloxone; naloxone is short acting and given mainly parenterally. So the claim that naloxone is more potent than naltrexone is FALSE.
Step 6: The question asks for the false statement, so option D is the answer.
Answer: Option D.