The way most companies handle cross-border payroll is to attach the remote worker to a department already in that country for legal/financial purposes and then put them "on assignment" across the border. This avoids expensive and complicated paperwork, letting the company move the money internally (much simpler) and then make normal payment. Simplifies the employee's taxes too, obviously.
(I spent several years based in Boston but assigned to the Toronto lab.)
If there isn't already an office in that country to play this roll, companies may not even want to try to have people working remotely from another country. The overhead is just too high for a single individual.
I have no idea whether/how this is affected by being a contractor rather than employee.