Fair value is defined as the amount for which an asset could be exchanged or a liability settled between knowledgeable, willing parties in an arm's length transaction. It is also the value for which an enterprise can take over another enterprise's liability.
If there is no independence between the fair value of liabilities and the assets used to meet these liabilities, then then this would place a bias in the values calculated. For example, if one were comparing the value of assets to liabilities of a benefit provider to assess solvency, then these values would not be a reliable reflection of the solvency position of the provider. A unit increase in the value of assets (of the provider) could cause some proportional increase the value of liabilities (due to dependency), but as we have seen with the liabilities of most providers, the cash flows show no dependency to assets but rather to external cash flows (e.g. the obligation to pay a lump sum upon survival at a certain term).
Also, if another company wishes to takeover the liabilities of the provider, and if the provider has a large pool of assets, then the fair value of liabilities may be objectively unreasonable from the opinion of the other company.