NO, they are trying to apply the doctrine CONSTRUCTIVE receipt in a very simplistic/administrative fashion, which the IRS follows for all cash basis taxpayers (which is what you are). It says the following.
For federal tax
purposes, the doctrine of constructive receipt is used to determine when a cash-basis taxpayer has received gross income (1) A taxpayer is subject to tax in the current year if he or she has unfettered control in determining when items of income will or should be paid. (2) However, unlike actual receipt, constructive receipt does not require physical possession of the item of income in question.
(That's what constructive means, you had it even though you didn't physically have it)
1. Samuel A. Donaldson, Federal Income Taxation
of Individuals: Cases, Problems and Materials, 353 (2nd Ed. 2007).
2. Treas. Reg. § 1.451-2(a).
So you see that the argument has two sides... You were completely entitled to the dollars in the earlier year, but the check date was in 2013, meaning you didn't have unfettered control.
Where you see constructive receipt come up a lot is where folks who get a paycheck after the first of the year still have to pay taxes on those dollars for the previous year, because the check date was for December (even though they had not physically received the dollars, IS will say that they CONSTRUCTIVELY received them.
Your argument here will need to turn on the fact that even though, ADMINISTRATIVELY, the check date is typically used to determine that $ are received, constructively
, in the previous year rather than the current year (again, typically used to KEEP people from deferring the income - and tax on it - into the next year) ... You were entitled to those dollars in the year that the work was done, as matter or both your contract (work for money) and ethically, as well.
They are relying on an administrative interpretation of constructive receipt. You will need to go deeper and use the LEGAL argument that says, the money was your property (owed to you as any accounts receivable would be , counted as an asset) and should have been paid in 2012.
You'll need to turn the constructive receipt on it's ear a little and say that in THIS case the date on the check isn't the issue, its the fact that the work was done in 2012 and you were entitled to the pay in 2012.
A TAX administrator will say (from a purely procedural standpoint) that if the check was dated 2013, the money was constructively received in 2013.. "that's the way we do it."
A tax attorney will say that, here, the check date isn't the accurate way to determine when the income became your property (and legally income IS property) .. "the income became your property when you did the work, and the company made a mistake in not paying as they should have ... a mistake to which they have admitted."
You want to get anything you can in writing.. emails, letters, etc. with the company (or it's agents... HR) stating that this is compensation for work done in 2012.