Granting SYSTEM access to local files on MachineA does not allow a process running as SYSTEM on MachineB to access those files. You would need to grant access to MachineB's active directory computer account, YourDomainName\MachineB$.
The approach that I normally used was to create a local account with the same name and password on both machines. Give it a complex password and set it to never expire. Then grant that user access to the share and folder permissions on MachineA. On MachineB set the scheduled task to run as that account.
You should also capture stdout and stderr for the scheduled task.