I'm not asking what the moral or ethical difference is. They're paying for engineering output, and if they are getting that output, why does it really matter whose fingers are typing it in?
I wouldn't see anything wrong with this, but I would be willing to bet that 99% of companies would not go along with it--for reasons I'm not sure I understand.
There's legal aspects to the employer-employee relationship that are different than the company-vendor relationship.
Even reporting the pay to the IRS as personal income would probably be legally problematic, because from a legal aspect a vendor is being paid for a service not an individual receiving income from an employer.
At the same time, you are correct that it doesn't matter who is typing it. One of my favorite setups I've worked under is where throwing it over the fence is explicit - where a small team of employees each has their own small team of contractors. The management doesn't care who does what, as long as the work gets done, so we were free to parcel work out to our contractors as we saw fit, and that the institutional knowledge stayed baked into our heads.