Final answer:
It is true that a parent company controlling debt retirement can use its resources to retire its own bonds, which is a strategic financial decision to reduce debt obligations and manage capital structure.
Step-by-step explanation:
The statement 'The parent, which controls all debt retirement for the consolidated entity, can use its available resources to purchase and retire its own bonds if they choose not to use the fair value option' is true. A parent company within a consolidated entity has the ability to manage its financial resources in various ways, including the retirement of its own debt instruments such as bonds. When a company decides not to use the fair value option, it can still engage in transactions to buy back and retire its bonds from the market, thereby removing them from circulation and reducing its overall debt obligations. This process is important for managing the company's capital structure and can affect its financial health and performance.