I can't fathom why people start shitting bricks when it comes to immigration rules. During college, all my friends, seniors and I worked using our SSN, sometimes with a valid EAD card, sometimes, without it. I clearly remember how people were talking nonsense like 'your gc, H-1 visa etc will be held and rejected' etc. It turns out, that wasn't correct. When your wife file for her taxes, the USCIS or IRS won't be verifying whether, how or when she started working. All the IRS will be caring about is if she paid her taxes or not. 

To cut this all short, I'd not sweat over it. If you're gonna go into minute details like "only people coming in from oversees"...etc. you might as well start scrutinizing yourself. This will ultimately lead to you screwing and jeopardizing your peaceful soul. 

Good luck.