I assume that so long as you're officially working out of an office in a location and the company won't change your payroll status, that's where you're working out of as far as taxing authorities are concerned no matter what the "public information" is. I'm guessing it's not even especially legit but very few entities are pushing on it at this point--except in cases like this one where there's a big advantage to employees pushing to switch their work location.

My concern is that I will file the New Jersey return and pay taxes on the money I earned while working and living there, and file the New York return and ask for my money back since I don’t live or work there, and if New York denies the refund, I’ll be paying taxes in both states.

It’s unclear at this point whether New Jersey will let New York claim all this taxable income or whether New Jersey will try to claim it for itself (it needs the money too). The tax rates are pretty similar in both states but my preference would be for the money to go to the state I actually live in.