> For example, the 3rd party does not loan the the funds to exercise, but directly pays the cost.

That wouldn't work. "Paying the cost" would immediately result in taxable income to the employee, instead of realizing the income a few years down the line when the debt is canceled.

There's no free lunch here. The 3rd party lost money too, because they couldn't collect the debt. If the 3rd party wanted to fully protect the employee, they could have sent an additional payment to cover the taxes. But that just means the 3rd party suffers a greater loss.