Well the first issue I see with this scenario is that if the settlement is for personal injuries, it is not earnings that are subject to income tax and other witholdings.
If the settlement is for lost wages or back pay (perhaps due to the injury? a work-related injury?) then it is considered income subject to taxes. "Grossing up" means that they took the desired net amount of $10K and added enough to it to make the gross = $XX. When taxes and withholdings were deducted from $XX, the net pay was $10K. Therefore you probably don't owe any more taxes on the $10K because they have already been deducted.
However, you still claim the entire amount of $XX as gross income on your tax return and the taxes withheld as, well, taxes withheld. There is no guarantee that you won't owe any additional taxes for the year. The settlement check should have a stub that explains the gross amount and deductions, just like a paycheck. The w-2 would reflect the gross amount of $XX.
Please note I am neither a tax professional nor a lawyer. I work for a law firm that handles employment law and PI cases and that is how I am familiar with this. Any information I provide is general in nature and I do not swear by its correctitude.