Final answer:
The false statement is that stock dividends declared but not yet distributed are reported as a liability; they should be recorded in shareholders' equity.
Step-by-step explanation:
The statement which is false among the options provided is: Stock dividends declared but not yet distributed are reported as a liability until the stock is issued. This is not correct as stock dividends represent a reallocation of equity rather than an obligation, and are therefore recorded in shareholders' equity, not as a liability on the balance sheet. On the contrary, the statements about a company being able to exclude a short-term obligation from current liabilities if it intends to refinance on a long-term basis, recording cash dividends as a liability when declared, and unearned revenues representing advance payments for goods or services are all true.