In order to pay off her $6000 loan, she'll have to take out from the 401k not only the $6000, but also enough to cover the income tax on the total amount of the distribution.

Sorry, this is not correct.

The money for the loan was already taken out of her account, so the only way that she can 'withdraw' the loan balance is to default on the payments. The question is - assuming she's still employed, will her employer allow her to stop taking those payments out of her paycheck so that she will default?

Also, if she were to withdraw the $13k and use some of the $13k to pay back the loan, she would now have a $6k balance in her account, and would not owe taxes or penalties on the $6k - just on the $13k. She would have to initiate another withdrawal to withdraw the $6k if she wanted that money out of the plan. Since plans often have pretty stringent rules about withdrawals, she may have to wait 6 months - 1 year (or more) in order to initiate that 2nd withdrawal.

AJ