It does not appear that the receiver would be absolutely certain that no bit errors have occurred. As long as the checksum and its 1s complement equal the value that was originally sent, it will verify. Basically, a 0 or 1 can possibly be swapped somewhere in the checksum, but no bit errors will be detected as long as the addition sent by the sender and checksum received by the receiver match. No, the receiver cannot be absolutely certain that no bit errors have occurred. This is because of the manner in which the checksum for the packet is calculated.
