Legality of flying as 'safety pilot'

[Level Attitude]

YOUR QUALIFICATIONS You should be checked out and current on the aircraft. Unless you have to take over the controls you are supernumerary and cannot log any flying time.

The above strongly suggests that if the Safety Pilot has to take over then they will log flight time. The only flight time they could log would be as PIC.

Therefore a Safety Pilot needs to be qualified to act as PIC in the aircraft under all expected flight conditions (Aeros, IMC, Night, etc). They cannot rely on the OSL Pilot's qualifications.