SD - whoever that was must have been an idiot! He/she clearly has no idea about flying instruction and supervision and is totally wrong!
If you have a SEP Class Rating (not a Type Rating), you can theoretically fly any SEP aeroplane. But if you are being supervised in such an aeroplane by a FI, your flight must be P1 under supervision. Obviously!! He/she is Commander, you are Pilot under Supervision.
However, if you were learning to fly a different Type (as defined) or a different Class of aeroplane, that would obviously be P u/t - you would be learning a new skill. As you would be if you were undergoing VP, SP, RG or TW difference training in aeroplanes of the same SEP Class .
Please remember these basic concepts - and DON'T assume that every pen-pusher at the Belgrano has the faintest idea about flying.