> If you have the cash to pay them off, then they don't get to say no even if it's a short sale.

If you actually pay them off, then they don't get to say no, because paying them off is, essentially, buying out their interest in the property, under the terms of an existing contract. That doesn't negate the fact that they have legally-enforceable rights in the property until and unless you do that.

> Alternatively, you can generally walk away and sell it to them for the value of the loan.

Only if the mortgage is governed by the law of a jurisdiction where pursuit of mortgage deficiency isn't allowed (either in general or for mortgages in the specific conditions yours has.)